Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Algebras and Smarandache Types

Version 1 : Received: 4 November 2018 / Approved: 5 November 2018 / Online: 5 November 2018 (12:53:07 CET)

How to cite: Kim, H.S.; Neggers, J.; Ahn, S.S. Algebras and Smarandache Types. Preprints 2018, 2018110117 (doi: 10.20944/preprints201811.0117.v1). Kim, H.S.; Neggers, J.; Ahn, S.S. Algebras and Smarandache Types. Preprints 2018, 2018110117 (doi: 10.20944/preprints201811.0117.v1).

Abstract

If an algebra of type $A$ contains a subalgebra which is also an algebra of type $B$, then it is a Smarandache $B$-type $A$-algebra provided the subalgebra of type $B$ contains at least two elements. This generalizes the notion of Smarandache group, where the group of order $\geq 2$ is a subsemigroup of a semigroup. In this paper we investigate a number of such pairings and we deduce a number of conclusions as a consequence.

Subject Areas

Smarandache algebra; point algebra; $p$-derived algebra.

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