Every quasitrivial n-ary semigroup is reducible to a semigroup

Every finite semigroup is embeddable in a finite relatively free semigroup

The title result is proved by a Murskii-type embedding. Results on some related questions are also obtained. For instance, it is shown that every finitely generated semigroup satisfying an identity ξ d = ξ2d is embeddable in a relatively free semigroup satisfying such an identity, generally with a larger d ; but that an uncountable semigroup may satisfy such an identity without being embeddable...

Neutrosophic Bi-LA-Semigroup and Neutrosophic N-LA- Semigroup

In this paper we define neutrosophic bi-LAsemigroup and neutrosophic N-LA-semigroup. Infact this paper is an extension of our previous paper neutrosophic left almost semigroup shortly neutrosophic LAsemigroup. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neu...

Every Group is a Maximal Subgroup of the Free Idempotent Generated Semigroup over a band

Given an arbitrary group G we construct a semigroup of idempotents (band) BG with the property that the free idempotent generated semigroup over BG has a maximal subgroup isomorphic to G. If G is finitely presented then BG is finite. This answers several questions from recent papers in the area.

Every Group Is a Maximal Subgroup of a Naturally Occurring Free Idempotent Generated Semigroup

The study of the free idempotent generated semigroup IG(E) over a biordered set E has recently received a deal of attention. Let G be a group, let n ∈ N with n ≥ 3 and let E be the biordered set of idempotents of the wreath product G ≀ Tn. We show, in a transparent way, that for e ∈ E lying in the minimal ideal of G ≀ Tn, the maximal subgroup of e in IG(E) is isomorphic to G. It is known that G...

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions