Some Results on the Relationship Between Smarandache Semigroups and Their Smarandache Subsemigroups
DOI:
https://doi.org/10.62054/ijdm/0102.08Keywords:
Smarandache semigroup, Smarandache subsemigroup, Smarandache inverse pair, Smarandache Lagrange semigroup, Smarandache weakly Lagrange semigroupAbstract
In a journal titled “Smarandache Semigroups” discussed Validity of Some Classical Theorems of Group Theory in case of Smarandache Semigroup and Smarandache notions in group. Padilla Raul, introduced the notion of smarandache semigroups, titled “Smarandache Algebraic Structures”. A smarandache semigroup is a semigroup A which has a proper subset B contained in A that is a group (with respect to the same binary operation on A ). The nature of the structure is extremely interesting and attractive, since it handles a weak and a strong structure. Here we shall be establishing some basic properties of smarandache semigroups. We studied some aspects of smarandache semigroups and used those facts to establish some basic properties of smarandache semigroup and smarandache notion in group. Let Zn = {1, 2, 3, . . ., n-1}. In this paper, we established some results about relationship that exists between Smarandache semigroups and Smarandache Subsemigroups. And some results on uniqueness of related pair of a Smarandache inverse pair and Smarandache weakly Lagrange semigroup on Z2n. Next, we have newly defined concepts: Smarandache Ideal of Smarandache semigroup, Smarandache weakly Cauchy semigroup
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