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Generalized F -semigroups

E. Giraldes, P. Marques-Smith, Heinz Mitsch (2005)

Mathematica Bohemica

A semigroup S is called a generalized F -semigroup if there exists a group congruence on S such that the identity class contains a greatest element with respect to the natural partial order ≤ S of S . Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup ( S , · , ≤ S ) are determined. It is shown that a semigroup S is a generalized F -semigroup if and only if S contains an anticone, which is a principal order ideal of ( S , ≤ S ) . Also a characterization by means of the structure...

Generalized free products

J. D. Monk (2001)

Colloquium Mathematicae

A subalgebra B of the direct product ∏ i ∈ I A i of Boolean algebras is finitely closed if it contains along with any element f any other member of the product differing at most at finitely many places from f. Given such a B, let B* be the set of all members of B which are nonzero at each coordinate. The generalized free product corresponding to B is the subalgebra of the regular open algebra with the poset topology on B* generated by the natural basic open sets. Properties of this product are developed....

Generalized homogeneous, prelattice and MV-effect algebras

Zdena Riečanová, Ivica Marinová (2005)

Kybernetika

We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra P are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We prove that every prelattice generalized effect algebra P is a union of generalized MV-effect algebras and...

Generalized prime D -filters of distributive lattices

A.P. Phaneendra Kumar, M. Sambasiva Rao, K. Sobhan Babu (2021)

Archivum Mathematicum

The concept of generalized prime D -filters is introduced in distributive lattices. Generalized prime D -filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime D -filters is introduced in distributive lattices and properties of minimal prime D -filters are then studied with respect to congruences. Some topological properties of the space of all prime D -filters of a distributive lattice are also studied.

Generalized versions of MV-algebraic central limit theorems

Piotr Nowak, Olgierd Hryniewicz (2015)

Kybernetika

MV-algebras can be treated as non-commutative generalizations of boolean algebras. The probability theory of MV-algebras was developed as a generalization of the boolean algebraic probability theory. For both theories the notions of state and observable were introduced by abstracting the properties of the Kolmogorov's probability measure and the classical random variable. Similarly, as in the case of the classical Kolmogorov's probability, the notion of independence is considered. In the framework...

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.

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