MATHEMATICA BOHEMICA, Vol. 128, No. 3, pp. 319-324 (2003)

Generalized deductive systems
in subregular varieties

Ivan Chajda

Ivan Chajda, Department of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail:

Abstract: An algebra $\A= (A,F)$ is subregular alias regular with respect to a unary term function $g$ if for each $\Theta, \Phi\in\CA$ 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).

Keywords: regular variety, subregular variety, deductive system, congruence class, difference system

Classification (MSC2000): 08A30, 08B05, 03B22

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