Introducing fully UP-semigroups

Abstract

In this paper, we introduce some new classes of algebras related to UP-algebras and semigroups, called a left UP-semigroup, a right UP-semigroup, a fully UP-semigroup, a left-left UP-semigroup, a right-left UP-semigroup, a left-right UP-semigroup, a rightright UP-semigroup, a fully-left UP-semigroup, a fully-right UP-semigroup, a left-fully UP-semigroup, a right-fully UP-semigroup, a fully-fully UP-semigroup, and find their examples.Mathematics Subject Classification: 08A99, 03G25

Neutrosophic Set Theory Applied to UP-Algebras

“…In particular, (P(X), •, ∅) is a UP-algebra and we shall call it the power UP-algebra of type 1, and (P(X), * , X) is a UP-algebra and we shall call it the power UP-algebra of type 2. For more examples of UP-algebras, see [1,6,20,21].…”

Anti-type of Hesitant Fuzzy Sets on UP-algebras

“…Proposition 1. [2,3] In a UP-algebra A = (A, •, 0), the following properties hold: Guntasow et al [1] proved the generalization that the notion of UP-subalgebras is a generalization of UP-filters, the notion of UP-filters is a generalization of UP-ideals, and the notion of UP-ideals is a generalization of strongly UP-ideals. Moreover, they also proved that a UP-algebra A is the only one strongly UP-ideal of itself.…”

Some Structural Properties of Fully UP-semigroups

“…A. Iampan [4] analogously introduced a left [resp., right] UP-semigroup as a nonempty set X together with two binary operations * and · and a constant 0 satisfying (f UP1), (f UP2), and the operation · is left [resp. right] distributive over the operation * .…”

“…[4] Let X = {0, a, b, c} be a set with the binary operations * and · defined by the following Cayley tables: * 0 a b c 0 X; * , ·, 0) is an f -UP-semigroup. Let X = {0, a, b, c} be a set with the binary operations * and · defined by the following Cayley tables: * 0 calculations show that (X; * , ·, 0) is an f -UP-semigroup.…”