Equational bases for weak monounary varieties

Grzegorz Bińczak

Discussiones Mathematicae - General Algebra and Applications (2002)

  • Volume: 22, Issue: 1, page 87-100
  • ISSN: 1509-9415

Abstract

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It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.

How to cite

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Grzegorz Bińczak. "Equational bases for weak monounary varieties." Discussiones Mathematicae - General Algebra and Applications 22.1 (2002): 87-100. <http://eudml.org/doc/287645>.

@article{GrzegorzBińczak2002,
abstract = {It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.},
author = {Grzegorz Bińczak},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {partial algebra; weak equation; weak variety; regular equation; regular weak equational theory; monounary algebras; partial algebras; weak equational theory},
language = {eng},
number = {1},
pages = {87-100},
title = {Equational bases for weak monounary varieties},
url = {http://eudml.org/doc/287645},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Grzegorz Bińczak
TI - Equational bases for weak monounary varieties
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2002
VL - 22
IS - 1
SP - 87
EP - 100
AB - It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.
LA - eng
KW - partial algebra; weak equation; weak variety; regular equation; regular weak equational theory; monounary algebras; partial algebras; weak equational theory
UR - http://eudml.org/doc/287645
ER -

References

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  1. [1] G. Bińczak, A characterization theorem for weak varieties, Algebra Universalis 45 (2001), 53-62. Zbl1039.08002
  2. [2] P. Burmeister, A Model - Theoretic Oriented Approach to Partial Algebras, Akademie-Verlag, Berlin 1986. Zbl0598.08004
  3. [3] G. Grätzer, Universal Algebra, (the second edition), Springer-Verlag, New York 1979. 
  4. [4] H. Höft, Weak and strong equations in partial algebras, Algebra Universalis 3 (1973), 203-215. Zbl0287.08003
  5. [5] E. Jacobs and R. Schwabauer, The lattice of equational classes of algebras with one unary operation, Amer. Math. Monthly 71 (1964), 151-155. Zbl0117.26003
  6. [6] L. Rudak, A completness theorem for weak equational logic, Algebra Universalis 16 (1983), 331-337. Zbl0519.08006
  7. [7] L. Rudak, Algebraic characterization of conflict-free varieties of partial algebras, Algebra Universalis 30 (1993), 89-100. Zbl0810.08003

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