Decomposition of a locally associative la-semigroup

On semilattice decomposition of an Abel-Grassmann’s groupoid

“…An AG-groupoid S is called locally associative if it satisfies (aa)a = a(aa), for all a in S. It has been proved in [11] that in a locally associative AG-groupoid S with left identity, aa n = a n a and (ab) n = a n b n hold for all a, b ∈ S. Also in [12] it has been proved that, if S is a locally associative AG-groupoid satisfying (3), then a n b m = b m a n holds for all a, b ∈ S and m, n ≥ 2, while these identities hold in commutative semigroups.…”

“…Then in [17] Yamada decomposed a semigroup into its archimedean components. Locally associative LAsemigroups and AG * -groupoids are decomposed in [11] and [1] respectively. In [18], Lizasoain has worked on "a decomposition theorem for G-groups".…”

Rough Approximations in Left Almost Groups

“…They introduced braces on the left of the ternary commutative law abc = cba, to get a new pseudo associative law, that is (ab)c = (cb)a, and named it as left invertive law. Later, Mushtaq [11][12][13][14][15] and others investigated the structure further and added many useful results to the theory of LA-semigroups. It was much later when Mushtaq and Kamran [5] in 1987 succeeded in defining a non-associative group which they called an LA-group and can be equally manipulated with as a subtractive group.…”

On Hyperideals in Left Almost Semihypergroups

“…They have generalized some useful results of semigroup theory. Since then, many papers on LA-semigroups appeared showing the importance of the concept and its applications [13][14][15][16][17][18][19][20][21][22][23] . In this paper, we generalize this notion introducing the notion of LAsemihypergroup which is a generalization of LA-semigroup and semihypergroup, proposing so a new kind of hyperstructure for further studying.…”