Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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01 Jan 2015
TL;DR: In this article, the notions of smarandache soft semigroups (SS-semigroups) were introduced for the first time, and an SS-semigroup was defined.
Abstract: In this paper, the notions of smarandache soft semigroups (SS-semigroups) introduced for the first time. An SS-semigroup
1 citations
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TL;DR: This work proves that the numerical-semigroup-gap counting problem is #NP-complete as a main theorem, and shows the # NP-completenesses of other two variants of the numerical, semigroup, gap counting problem.
Abstract: In this paper, we prove that the numerical-semigroup-gap counting problem is #NP-complete as a main theorem. A numerical semigroup is an additive semigroup over the set of all nonnegative integers. A gap of a numerical semigroup is defined as a positive integer that does not belong to the numerical semigroup. The computation of gaps of numerical semigroups has been actively studied from the 19th century. However, little has been known on the computational complexity. In 2005, Ramirez-Alfonsin proposed a question whether or not the numerical-semigroup-gap counting problem is #P-complete. This work is an answer for his question. For proving the main theorem, we show the #NP-completenesses of other two variants of the numerical-semigroup-gap counting problem.
1 citations
1 citations
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01 Jan 1977
TL;DR: The theory of homotopy of universal algebras has been studied in this article, where a complete description of monomorphisms and epimorphisms in a category of quasigroups whose morphisms are homotopies is given.
Abstract: Publisher Summary This chapter describes the theory of homotopy of universal algebras. The concept of isotopy occupies a central place in the theory of quasigroups and in the theory of projective planes. The chapter discusses homotopies of some classical algebraic systems as quasigroups, equasigroups, groups, rings, and lattices. It presents a complete description of monomorphisms and epimorphisms in a category of quasigroups whose morphisms are homotopies. It is assumed that A is algebra. Under the composition of homotopies H(A, A) is a semigroup with unit element, the endotopy semigroup of A, and the set of all autotopies of A is a group, the autotopy group of A. Every semigroup that has a unit element is isomorphic to the endotopy semigroup of a suitable algebra. Every group is isomorphic to an autotopy group of some algebra. Every semigroup that has a unit element is isomorphic to the endotopy semigroup of a suitable algebra.
1 citations