Note that S is non-void because if we fix s [member of] S, S contains the commutative semigroup
<s> generated by s which is countable an amenable.
A commutative semigroup
is a semigroup with a commutative operation.
An LA-semigroup is a non-associative algebraic structure that is generally considered as a midway between a groupoid and a commutative semigroup
but is very close to commutative semigroup
because most of their properties are similar to commutative semigroup
AG-groupoids generalizes the concept of commutative semigroup
and have an important application within the theory of flocks.
A, [cross product]) is a commutative semigroup
with ([for all] x [member of] A) (x [cross product] x = x), where the semigroup operation is strongly extensional:
Our aim in this paper is to develop some characterizations for a new non-associative algebraic structure known as a left almost semigroup which is the generalization of a commutative semigroup
Gilmer, Commutative semigroup
rings, the University of Chicago Press, Chicago, Illinois 1984.
An Abel- Grassmann's groupoid, abbreviated as an AG-groupoid (or in some papers left almost semigroup), is a non-associative algebraic structure mid way between a groupoid and a commutative semigroup
Let G be a Smarandache Groupoid, G is said to be a Smarandache commutative groupoid if there is a proper subset, which is a semigroup, is a commutative semigroup
An LA-semigroup is basically a midway structure between a groupoid and a commutative semigroup
3) For all e [member of] E(S),eSe is a commutative semigroup
In commutative semigroup
the prime and weakly Prime ideals coincide.