In this paper, a new approach to LA-semigroup theory is proposed by obtaining significant characterizations of regular, intra-regular, completely regular, weakly regular and quasi-regular LA-semigroups via soft intersection left (right, two-sided) ideals, (generalized) bi-ideals, interior ideals, quasi-ideals of LA-semigroups.

In this paper we establish Strichartz type estimates associated with a class of semigroup operators in Rn, which for n = 2 correspond to some 2D water wave models. We also establish a nonlinear scattering result for solutions of the generalized Benney-Luke equation for higher order nonlinearity and small data initial in the energy space.

We give an upper bound of n((n−1)!−(n−3)!) for the possi5 ble largest size of a subsemigroup of the full transformational semigroup 6 over n elements consisting only of nonpermutational transformations. As 7 an application we gain the same upper bound for the syntactic complex8 ity of (generalized) definite languages as well. 9

The concept of q , -fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by q , -fuzzy left (right, lateral) ideals, q , -fuzzy quasi-ideals and q , -fuzzy bi-(generalized bi-) ideals.

We establish topological properties of the topological symmetric inverse semigroup of finite transformations I n λ of the rank 6 n. We show that the topological inverse semigroup I n λ is algebraically closed in the class of topological inverse semigroups. Many topologists established topological property of topological spaces of partial continuous maps PC (X, Y ) from a topological space X int...