Generalized deductive systems in subregular varieties

@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 -