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Quotient algebraic structures on the set of fuzzy numbers

Dorina Fechete, Ioan Fechete (2015)

Kybernetika

A. M. Bica has constructed in [6] two isomorphic Abelian groups, defined on quotient sets of the set of those unimodal fuzzy numbers which have strictly monotone and continuous sides. In this paper, we extend the results of above mentioned paper, to a larger class of fuzzy numbers, by adding the flat fuzzy numbers. Furthermore, we add the topological structure and we characterize the constructed quotient groups, by using the set of the continuous functions with bounded variation, defined on [ 0 , 1 ] .

Quotients and homomorphisms of relational systems

Ivan Chajda, Helmut Länger (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Relational systems containing one binary relation are investigated. Quotient relational systems are introduced and some of their properties are characterized. Moreover, homomorphisms, strong mappings and cone preserving mappings are introduced and the interplay between these notions is considered. Finally, the connection between directed relational systems and corresponding groupoids is investigated.

Radical decompositions of semiheaps

Ian Hawthorn, Tim Stokes (2009)

Commentationes Mathematicae Universitatis Carolinae

Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of various classes of idempotent semiheaps are given. The results are applied to involuted I-semigroups, leading...

Rees ideal algebras

Ivan Chajda (1997)

Mathematica Bohemica

We describe algebras and varieties for which every ideal is a kernel of a one-block congruence.

Regular elements and Green's relations in Menger algebras of terms

Klaus Denecke, Prakit Jampachon (2006)

Discussiones Mathematicae - General Algebra and Applications

Defining an (n+1)-ary superposition operation S n on the set W τ ( X n ) of all n-ary terms of type τ, one obtains an algebra n - c l o n e τ : = ( W τ ( X n ) ; S n , x 1 , . . . , x n ) of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation S n there are different possibilities to define binary associative operations on the set W τ ( X n ) and on the cartesian power W τ ( X n ) n . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative operations...

Regular lattices

Ivan Chajda (1993)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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