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

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 lefte-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 lefte-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 ifit 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 andcharacterize all the identical magma-e-magmas in several ways. The motivation of this study lies in some interesting connectionsto f-multiplications, some basic functional equations on algebraic structures and Grouplikes (recently introduced by me). Finally, Ipresent some directions for the researches conducted on the sub- ject

کلیدواژه ها:

Algebraic structure ، Grouplike ، Magma