In this note, we show in the line of [3] that an ordered Γ-semigroup is left and right simple if and only if it does not contain proper bi-ideals. Mathematics Subject Classification: 06F99

Let R be a commutative ring with nonzero identity. A proper ideal I of is said to 1-absorbing prime if xyz ∈ for some nonunits x, y, z R, then xy or I. It well known that ⇒ primary semi-primary ideal, is, the class ideals comes between classes and ideals. Also, above right arrows are not reversible. In this article, we characterize rings over which every prime. by comparing other classical such...

Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B := A[[y;α]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A and B are equal. We also record applications to induced ideals.

In this paper, we establish some equivalent conditions for a semigroup to be regular and intra-regular, in terms of hybrid ideals bi-ideals. We also characterize the left right simple completely semigroups utilizing show that S is if only it simple. prove then each ideal ˜jµ S, have ˜jµ(r1r2) = ˜jµ(r2r1) all r1, r2 ∈ S.

1. Let F be a partially ordered vector space with an order unit e. It is well known that the class 5DÎ of maximal ideals of V is in one-one correspondence with the class K of normalized positive linear functionals, in the sense that to each ME^SR corresponds a positive linear functional <¡>m with M as its null-space and with M(e) = 1. A maximal ideal MG 90? is said to be extreme if <pM is an...

s of papers presented at the meeting follow. Abstracts whose titles are followed by "t" were presented by title. Mrs. Lehmer was introduced by the Associate Secretary, Mr. Rail by Professor Lonseth, Professor Nash by Professor W. T. Martin, and Mr. Krabble by Professor C. B. Morrey. ALGEBRA AND THEORY OF NUMBERS 5SSt. W. E. Barnes: Primal ideals in noncommutative rings. In any associative ring ...

In this paper S will denote an AG-groupoid. A two-sided ideal I of S is called a right (left) pure ideal of S , if for each x in I , there is an element y in I such that ) = ( = x yx x xy . A left (right) pure ideal I is called purely prime if it is proper and if for any pure ideals 1 I and 2 I : I I I 2 1 implies I I1 or I I2 . Analogous to the construction of the pure spectrum of a semigroup ...

We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over GR(4) are constr...

Let R be a nil ring. We prove that primitive ideals in the polynomial ring R[x] in one indeterminate over R are of the form I [x] for some ideals I of R. All considered rings are associative but not necessarily have identities. Köthe’s conjecture states that a ring without nil ideals has no one-sided nil ideals. It is equivalent [4] to the assertion that polynomial rings over nil rings are Jaco...