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Generalized deductive systems in subregular varieties

Ivan Chajda (2003)

Mathematica Bohemica

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).

Generalized inflations and null extensions

Qiang Wang, Shelly L. Wismath (2004)

Discussiones Mathematicae - General Algebra and Applications

An inflation of an algebra is formed by adding a set of new elements to each element in the original or base algebra, with the stipulation that in forming products each new element behaves exactly like the element in the base algebra to which it is attached. Clarke and Monzo have defined the generalized inflation of a semigroup, in which a set of new elements is again added to each base element, but where the new elements are allowed to act like different elements of the base, depending on the context...

Generated fuzzy implications and fuzzy preference structures

Vladislav Biba, Dana Hliněná (2012)

Kybernetika

The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet ( p , i , j ) , which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.

Generating methods for principal topologies on bounded lattices

Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu (2021)

Kybernetika

In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.

Graphic algebras

Ladislav Nebeský (1970)

Commentationes Mathematicae Universitatis Carolinae

Green's relations and their generalizations on semigroups

Kar-Ping Shum, Lan Du, Yuqi Guo (2010)

Discussiones Mathematicae - General Algebra and Applications

Green's relations and their generalizations on semigroups are useful in studying regular semigroups and their generalizations. In this paper, we first give a brief survey of this topic. We then give some examples to illustrate some special properties of generalized Green's relations which are related to completely regular semigroups and abundant semigroups.

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