TY - JOUR ID - 616 TI - MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Hooshmand, M. H. AD - Young Researchers and Elite Club, Shiraz Branch, Islamic Azad University, Shiraz, Iran. Y1 - 2015 PY - 2015 VL - 3 IS - 2 SP - 171 EP - 199 KW - 08A99 KW - 20N02 KW - 20M99 KW - 20N05 DO - 10.22044/jas.2015.616 N2 - By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif 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 basicalgebraic structures with two binary operations which some of theirsub-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 characterizeall 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 directionsfor the researches. UR - https://jas.shahroodut.ac.ir/article_616.html L1 - https://jas.shahroodut.ac.ir/article_616_129e9f74cb580b363d2f9eb90a41a37f.pdf ER -