MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES

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HOOSHMAND M.H.

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Journal: JOURNAL OF ALGEBRAIC SYSTEMS Year:2016 | Volume:3 | Issue:2 Page(s): 171-199

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Information Journal Paper

Title

MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES

Author(s)

HOOSHMAND M.H. | Issue Writer Certificate

Keywords

Algebraic structure

Grouplike

Magma

Abstract

By left Magma-e-Magma, I mean a set containing a xed element e, and equipped with the two binary operations \ " and ⊙ , with the property of e⊙ (x y) = e⊙ (x⊙ y), namely the left e-join law. Thus (X; ; e; ⊙ ) is a left Magma-e-Magma if and only if (X; ) and (X; ⊙ ) are Magmas (groupoids), e 2 X and the left e-join law holds. The right and two-sided Magma-e-Magmas are de ned in an analogous way. Also X is a Magma-joined-Magma if it is Magma-x-Magma for all x 2 X. Therefore, I introduce a big class of basic Algebraic structures with two binary operations, some of whose sub-classes are group-e-semigroups, loop-e-semigroups, semigroup-e-quasigroups and etc. A nice in nite (resp. nite) example of them is the real group-Grouplike (R; +; 0; +1) (resp. Klein group-Grouplike). In this paper, I introduce and study the topic, construct several big classes of such Algebraic structures and characterize all the identical Magma-e-Magmas in several ways. The motivation of this study lies in some interesting connections to f-multiplications, some basic functional equations on Algebraic structures and Grouplikes (recently introduced by me). Finally, I present some directions for the researches conducted on the sub-ject.

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APA: Copy

HOOSHMAND, M.H.. (2016). MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES. JOURNAL OF ALGEBRAIC SYSTEMS, 3(2 ), 171-199. SID. https://sid.ir/paper/268378/en

Vancouver: Copy

HOOSHMAND M.H.. MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2016;3(2 ):171-199. Available from: https://sid.ir/paper/268378/en

IEEE: Copy

M.H. HOOSHMAND, “MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 3, no. 2 , pp. 171–199, 2016, [Online]. Available: https://sid.ir/paper/268378/en

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