MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES | ||
| Journal of Algebraic Systems | ||
| مقاله 7، دوره 3، شماره 2، فروردین 2016، صفحه 171-199 اصل مقاله (201.83 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2015.616 | ||
| نویسنده | ||
| M. H. Hooshmand* | ||
| Young Researchers and Elite Club, Shiraz Branch, Islamic Azad University, Shiraz, Iran. | ||
| چکیده | ||
| By left magma-$e$-magma, I mean a set containing the fixed element $e$, and equipped by two binary operations "$cdot$" , $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namely left $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magma if and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds. Right (and two-sided) magma-$e$-magmas are defined in an analogous way. Also, $X$ is magma-joined-magma if it is magma-$x$-magma, for all $xin X$. Therefore, we introduce a big class of basic algebraic structures with two binary operations which some of their sub-classes are group-$e$-semigroups, loop-$e$-semigroups, semigroup-$e$-quasigroups, etc. A nice infinite [resp. finite] example for them is real group-grouplike $(mathbb{R},+,0,+_1)$ [resp. Klein group-grouplike]. In this paper, I introduce and study the topic, construct several big classes of such algebraic structures and characterize all identical magma-$e$-magma 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 been introduced by the author). At last, we show some of future directions for the researches. | ||
| کلیدواژهها | ||
| 08A99؛ 20N02؛ 20M99؛ 20N05 | ||
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