By left magma--magma, I mean a set containing the fixed element , and equipped by two binary operations "" , with the property , namely left -join law. So, is a left magma--magma if and only if , are magmas (groupoids), and the left -join law holds. Right (and two-sided) magma--magmas are defined in an analogous way. Also, is magma-joined-magma if it is magma--magma, for all . Therefore, we introduce a big class of basic algebraic structures with two binary operations which some of their sub-classes are group--semigroups, loop--semigroups, semigroup--quasigroups, etc. A nice infinite [resp. finite] example for them is real group-grouplike [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--magma in several ways. The motivation of this study lies in some interesting connections to -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.
Hooshmand, M. H. (2015). MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES. Journal of Algebraic Systems, 3(2), 171-199. doi: 10.22044/jas.2015.616
MLA
Hooshmand, M. H. . "MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES", Journal of Algebraic Systems, 3, 2, 2015, 171-199. doi: 10.22044/jas.2015.616
HARVARD
Hooshmand, M. H. (2015). 'MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES', Journal of Algebraic Systems, 3(2), pp. 171-199. doi: 10.22044/jas.2015.616
CHICAGO
M. H. Hooshmand, "MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES," Journal of Algebraic Systems, 3 2 (2015): 171-199, doi: 10.22044/jas.2015.616
VANCOUVER
Hooshmand, M. H. MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES. Journal of Algebraic Systems, 2015; 3(2): 171-199. doi: 10.22044/jas.2015.616
)