A theory of extensions of quasi-algebras to algebras

J. Słomiński

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1964

Abstract

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CONTENTSINTRODUCTION...................................................................................................................................................................... 31. TERMS NOTATION AND LEMMAS.................................................................................................................................. 4A. Quasi-algebras and algebras....................................................................................................................................................................... 4B. Subquasi-algebras and sets of generators............................................................................................................................................... 4C. Homomorphisms of quasi-algebras.......................................................................................................................................................... 5D. Direct. products quasi-algebras and homomorphisms.......................................................................................................................... 10E. Congruences of quasi-algebras and homomorphisms.......................................................................................................................... 10F. Terms and equations...................................................................................................................................................................................... 14G. Analytical operations defined by terms in quasi-algebras...................................................................................................................... 15H. Tensor product of quasi-algebras................................................................................................................................................................ 16I. The general transposition law of operations and algebras of homomorphisms and of bilinears of quasi-algebras.................. 17J. The form of congruences determined by terms......................................................................................................................................... 20§ 2. ON EXTENDING QUASI-ALGEBRAS TO ALGEBRAS............................................................................................................................ 21§ 3. ON THE COMMON EXTENSION OF QUASI-ALGEBRAS TO ALGEBRAS.......................................................................................... 30§ 4. A THEORY OF EXTENSIONS OF MAP-SYSTEMS IN EQUATIONALLY DEFINABLE CLASSES OF ALGEBRAS........................ 33A. Map-systems in equationally definable clauses of algebras.................................................................................................................. 33B. Quasi-ideals and ideals in A-map-systems...................................................................................................................... 35C. On dividing map-systems by ideals............................................................................................................................................................ 41D. Operator-systems in equationally definable classes of algebras......................................................................................................... 43E. The equivalence of the notions of quasi-ideals and ideals for A-operator-systems over R..................................... 45§ 5. ALGEBRAS WITH DIFFERENTIAL OPERATORS................................................................................................................................... 52A. Algebras with differential operators over commutative, algebras R...................................................................................................... 53B. Algebras with differential operators in the classes in which the general transposition law of operations holds........................ 54References............................................................................................................................................................................................................ 61

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J. Słomiński. A theory of extensions of quasi-algebras to algebras. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1964. <http://eudml.org/doc/268560>.

@book{J1964,
abstract = {CONTENTSINTRODUCTION...................................................................................................................................................................... 31. TERMS NOTATION AND LEMMAS.................................................................................................................................. 4A. Quasi-algebras and algebras....................................................................................................................................................................... 4B. Subquasi-algebras and sets of generators............................................................................................................................................... 4C. Homomorphisms of quasi-algebras.......................................................................................................................................................... 5D. Direct. products quasi-algebras and homomorphisms.......................................................................................................................... 10E. Congruences of quasi-algebras and homomorphisms.......................................................................................................................... 10F. Terms and equations...................................................................................................................................................................................... 14G. Analytical operations defined by terms in quasi-algebras...................................................................................................................... 15H. Tensor product of quasi-algebras................................................................................................................................................................ 16I. The general transposition law of operations and algebras of homomorphisms and of bilinears of quasi-algebras.................. 17J. The form of congruences determined by terms......................................................................................................................................... 20§ 2. ON EXTENDING QUASI-ALGEBRAS TO ALGEBRAS............................................................................................................................ 21§ 3. ON THE COMMON EXTENSION OF QUASI-ALGEBRAS TO ALGEBRAS.......................................................................................... 30§ 4. A THEORY OF EXTENSIONS OF MAP-SYSTEMS IN EQUATIONALLY DEFINABLE CLASSES OF ALGEBRAS........................ 33A. Map-systems in equationally definable clauses of algebras.................................................................................................................. 33B. Quasi-ideals and ideals in A-map-systems...................................................................................................................... 35C. On dividing map-systems by ideals............................................................................................................................................................ 41D. Operator-systems in equationally definable classes of algebras......................................................................................................... 43E. The equivalence of the notions of quasi-ideals and ideals for A-operator-systems over R..................................... 45§ 5. ALGEBRAS WITH DIFFERENTIAL OPERATORS................................................................................................................................... 52A. Algebras with differential operators over commutative, algebras R...................................................................................................... 53B. Algebras with differential operators in the classes in which the general transposition law of operations holds........................ 54References............................................................................................................................................................................................................ 61},
author = {J. Słomiński},
keywords = {general algebraic structures},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {A theory of extensions of quasi-algebras to algebras},
url = {http://eudml.org/doc/268560},
year = {1964},
}

TY - BOOK
AU - J. Słomiński
TI - A theory of extensions of quasi-algebras to algebras
PY - 1964
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSINTRODUCTION...................................................................................................................................................................... 31. TERMS NOTATION AND LEMMAS.................................................................................................................................. 4A. Quasi-algebras and algebras....................................................................................................................................................................... 4B. Subquasi-algebras and sets of generators............................................................................................................................................... 4C. Homomorphisms of quasi-algebras.......................................................................................................................................................... 5D. Direct. products quasi-algebras and homomorphisms.......................................................................................................................... 10E. Congruences of quasi-algebras and homomorphisms.......................................................................................................................... 10F. Terms and equations...................................................................................................................................................................................... 14G. Analytical operations defined by terms in quasi-algebras...................................................................................................................... 15H. Tensor product of quasi-algebras................................................................................................................................................................ 16I. The general transposition law of operations and algebras of homomorphisms and of bilinears of quasi-algebras.................. 17J. The form of congruences determined by terms......................................................................................................................................... 20§ 2. ON EXTENDING QUASI-ALGEBRAS TO ALGEBRAS............................................................................................................................ 21§ 3. ON THE COMMON EXTENSION OF QUASI-ALGEBRAS TO ALGEBRAS.......................................................................................... 30§ 4. A THEORY OF EXTENSIONS OF MAP-SYSTEMS IN EQUATIONALLY DEFINABLE CLASSES OF ALGEBRAS........................ 33A. Map-systems in equationally definable clauses of algebras.................................................................................................................. 33B. Quasi-ideals and ideals in A-map-systems...................................................................................................................... 35C. On dividing map-systems by ideals............................................................................................................................................................ 41D. Operator-systems in equationally definable classes of algebras......................................................................................................... 43E. The equivalence of the notions of quasi-ideals and ideals for A-operator-systems over R..................................... 45§ 5. ALGEBRAS WITH DIFFERENTIAL OPERATORS................................................................................................................................... 52A. Algebras with differential operators over commutative, algebras R...................................................................................................... 53B. Algebras with differential operators in the classes in which the general transposition law of operations holds........................ 54References............................................................................................................................................................................................................ 61
LA - eng
KW - general algebraic structures
UR - http://eudml.org/doc/268560
ER -

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