Generalized deductive systems in subregular varieties

Ivan Chajda

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 3, page 319-324
  • ISSN: 0862-7959

Abstract

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An algebra 𝒜 = ( A , F ) is subregular alias regular with respect to a unary term function g if for each Θ , Φ ∈ Con 𝒜 we have Θ = Φ whenever [ g ( a ) ] Θ = [ g ( a ) ] Φ for each a ∈ A . We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset C ⊆ A is a class of some congruence on Θ containing g ( a ) if and only if C is this generalized deductive system. This method is efficient (needs a finite number of steps).

How to cite

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Chajda, Ivan. "Generalized deductive systems in subregular varieties." Mathematica Bohemica 128.3 (2003): 319-324. <http://eudml.org/doc/249232>.

@article{Chajda2003,
abstract = {An algebra $\{\mathcal \{A\}\}= (A,F)$ is subregular alias regular with respect to a unary term function $g$ if for each $\Theta , \Phi \in \text\{Con\}\,\{\mathcal \{A\}\}$ we have $\Theta = \Phi $ whenever $[g(a)]_\{\Theta \} = [g(a)]_\{\Phi \}$ for each $a\in A$. We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset $C\subseteq A$ is a class of some congruence on $\Theta $ containing $g(a)$ if and only if $C$ is this generalized deductive system. This method is efficient (needs a finite number of steps).},
author = {Chajda, Ivan},
journal = {Mathematica Bohemica},
keywords = {regular variety; subregular variety; deductive system; congruence class; difference system; regular variety; subregular variety; deductive system; congruence class; difference system},
language = {eng},
number = {3},
pages = {319-324},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized deductive systems in subregular varieties},
url = {http://eudml.org/doc/249232},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Chajda, Ivan
TI - Generalized deductive systems in subregular varieties
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 3
SP - 319
EP - 324
AB - An algebra ${\mathcal {A}}= (A,F)$ is subregular alias regular with respect to a unary term function $g$ if for each $\Theta , \Phi \in \text{Con}\,{\mathcal {A}}$ we have $\Theta = \Phi $ whenever $[g(a)]_{\Theta } = [g(a)]_{\Phi }$ for each $a\in A$. We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset $C\subseteq A$ is a class of some congruence on $\Theta $ containing $g(a)$ if and only if $C$ is this generalized deductive system. This method is efficient (needs a finite number of steps).
LA - eng
KW - regular variety; subregular variety; deductive system; congruence class; difference system; regular variety; subregular variety; deductive system; congruence class; difference system
UR - http://eudml.org/doc/249232
ER -

References

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  5. 10.1007/s10012-000-0015-8, Southeast Asian Bull. Math. 24 (2000), 15–18. (2000) Zbl0988.08002MR1811209DOI10.1007/s10012-000-0015-8
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  8. Sulla varietá di algebre con una buona teoria degli ideali, Boll. Unione Mat. Ital. 6 (1972), 90–95. (1972) MR0314728

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