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Presolid varieties of n-semigroups

Avapa Chantasartrassmee, Jörg Koppitz (2005)

Discussiones Mathematicae - General Algebra and Applications

he class of all M-solid varieties of a given type t forms a complete sublattice of the lattice ℒ(τ) of all varieties of algebrasof type t. This gives a tool for a better description of the lattice ℒ(τ) by characterization of complete sublattices. In particular, this was done for varieties of semigroups by L. Polák ([10]) as well as by Denecke and Koppitz ([4], [5]). Denecke and Hounnon characterized M-solid varieties of semirings ([3]) and M-solid varieties of groups were characterized by Koppitz...

Prime Ideal Theorems and systems of finite character

Marcel Erné (1997)

Commentationes Mathematicae Universitatis Carolinae

We study several choice principles for systems of finite character and prove their equivalence to the Prime Ideal Theorem in ZF set theory without Axiom of Choice, among them the Intersection Lemma (stating that if S is a system of finite character then so is the system of all collections of finite subsets of ⋃ S meeting a common member of S ), the Finite Cutset Lemma (a finitary version of the Teichm“uller-Tukey Lemma), and various compactness theorems. Several implications between these statements...

Projection representable relations on Menger ( 2 , n ) -semigroups

Wiesław Aleksander Dudek, Valentin S. Trokhimenko (2008)

Czechoslovak Mathematical Journal

Abstract characterizations of relations of nonempty intersection, inclusion end equality of domains for partial n -place functions are presented. Representations of Menger ( 2 , n ) -semigroups by partial n -place functions closed with respect to these relations are investigated.

Projections of relations

Jiří Karásek (1995)

Mathematica Bohemica

A projection of a relation is defined as a relation of reduced arity. The paper deals with projections of relations in coherence with their reflexivity, symmetry, completeness, regularity, cyclicity and other properties. Relationships between projections of hulls and hulls of projections are also studied.

Pseudocomplements in sum-ordered partial semirings

Jānis Cīrulis (2007)

Discussiones Mathematicae - General Algebra and Applications

We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several...

Pure filters and stable topology on BL-algebras

Esfandiar Eslami, Farhad Kh. Haghani (2009)

Kybernetika

In this paper we introduce stable topology and F -topology on the set of all prime filters of a BL-algebra A and show that the set of all prime filters of A , namely Spec( A ) with the stable topology is a compact space but not T 0 . Then by means of stable topology, we define and study pure filters of a BL-algebra A and obtain a one to one correspondence between pure filters of A and closed subsets of Max( A ), the set of all maximal filters of A , as a subspace of Spec( A ). We also show that for any filter...

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