A ring R is called a right Ikeda-Nakayama (for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if (I ∩ J) = (I) + (J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f (x) = a0 + a1x + ··· + amx, g(x) = b0 + b1x + ··· + bnx ∈ R[x] satisfy f (x)g(x) = 0, then aibj = 0 for each ...

Definition 1.1. Let A be an involutive algebra over C with involution ξ 7→ ξ (resp. ξ 7→ ξ). We say A is a left (resp. right) Hilbert algebra if A has a inner product (· | ·) satisfying: a. Multiplication on the left (resp. right) is a bounded operator; that is, ∀ξ ∈ A the map πl(ξ) : η 7→ ξη (resp. πr(ξ) : η 7→ ηξ) is bounded on A. b. (ξη | ζ) = (η | ξζ) (resp. (ξη | ζ) = (ξ | ζη)). c. The inv...

Most of the results on semigroups or ordered can be transferred to hypersemigroups hypersemigroups, respectively. The same, if we replace word "semigroup" by "groupoid", "hypersemigroup" "hypergroupoid". We show way pass from fuzzy hypersemigroups.

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.

The intersection of all two-sided ideals of an ordered semigroup, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup (S, ·,≤) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L′ of (S, ·,≤), I is properly contained in L′ and L′ is contained in L imply L′ = L. The notions of simple right and two-s...

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨qk)-fuzzy ideals, (∈,∈ ∨qk)-fuzzy bi-ideals and (∈,∈ ∨qk)-fuzzy generalized bi-ideals of an ordered semigroup S by the ordered fuzzy points of S, and investigate their related properties. Furthermore, characterizations of regular ordered semigroups by the properties of (∈,∈ ∨qk)-fuzzy left ideals, (∈,∈ ∨qk)-fu...

Let k and n be integers such that k > 2n > 0. Let M be the complex analytic manifold defined by M = {x ∈ C : xx = 0, rank (x) = n}. Let G = SO(k,C) and G = GL(n,C), then Witt’s theorem on quadratic forms implies that G is a maximal connected Lie group acting transitively on M by right multiplication. Also, G is a maximal connected Lie group acting freely on M by left multiplication. If f ∈ C(M)...