Ring-like operations is pseudocomplemented semilattices

Ivan Chajda; Helmut Länger

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 1, page 87-95
  • ISSN: 1509-9415

Abstract

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Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.

How to cite

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Ivan Chajda, and Helmut Länger. "Ring-like operations is pseudocomplemented semilattices." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 87-95. <http://eudml.org/doc/287609>.

@article{IvanChajda2000,
abstract = {Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.},
author = {Ivan Chajda, Helmut Länger},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {pseudocomplemented semilattice; Boolean algebra; Boolean ring; distributivity; linear equation; ideal; congruence kernel; pseudocomplemented semilattices},
language = {eng},
number = {1},
pages = {87-95},
title = {Ring-like operations is pseudocomplemented semilattices},
url = {http://eudml.org/doc/287609},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Ivan Chajda
AU - Helmut Länger
TI - Ring-like operations is pseudocomplemented semilattices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 1
SP - 87
EP - 95
AB - Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
LA - eng
KW - pseudocomplemented semilattice; Boolean algebra; Boolean ring; distributivity; linear equation; ideal; congruence kernel; pseudocomplemented semilattices
UR - http://eudml.org/doc/287609
ER -

References

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  1. [1] I. Chajda, Pseudosemirings induced by ortholattices, Czechoslovak Math. J. 46 (121) (1996), 405-411. Zbl0879.06003
  2. [2] G. Dorfer, A. Dvurecenskij and H. Länger, Symmetric difference in orthomodular lattices, Math. Slovaca 46 (1996), 435-444. Zbl0890.06006
  3. [3] D. Dorninger, H. Länger and M. Maczyński, The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232. Zbl0879.06005
  4. [4] O. Frink, Pseudo-complements in semi-lattices, Duke Math. J. 29 (1962), 505-514. Zbl0114.01602
  5. [5] H. Länger, Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 97-105. Zbl0939.03075
  6. [6] A.I. Mal'cev, On the general theory of algebraic systems (Russian), Mat. Sb. 35 (1954), 3-20. 

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