Malaysian Journal of Mathematical Sciences, September 2020, Vol. 14, No. 3
Introducing Fuzzy Almost \(m\)-Ideals, Fuzzy Generalized Almost \(m\)-Ideals and Related Objects in Semigroups
Munir, M., Kausar, N., Addis, G. M., Salahuddin, and Anjum, R.
Corresponding Email: kausar.nasreen57@gmail.com
Received date: 11 June 2020
Accepted date: 10 August 2020
Abstract:
In this article, we present the concepts of almost m-ideals, generalized almost m-ideals, fuzzy almost m-ideals and fuzzy generalized almost \(m\)-ideals. We present the results illustrating their mutual differences, and similarities. Along these lines, we bring about their examples, and then characterize semigroups through their properties. One of the distinguished properties of the almost \(m\)-ideals respectively the related objects is that their intersection is not an almost \(m\)-ideal respectively related objects, while their union is. A subsemigroup of a semigroup is the almost \(m\)-ideals if and only if its charateristic function is the fuzzy almost \(m\)-ideals. Through these four closely related concepts of \(m\)-ideals, we show that this field will open new avenues of research and applications of semigroups.
Keywords: \(m\)-ideals, maximal almost \(m\)-ideal, fuzzy almost \(m\)-ideals, irreducible almost \(m\)-ideals
Indexing
