There exists an analogy between the structure of ideals of a cone in a right-ordered group and the structure of ideals of a Dubrovin valuation ring in a simple artinian ring. The structure of ideals of rank one cones and rank one Dubrovin valuation rings can be described completely. One sided versions of this problem are considered in 5] where the ideal theory of right cones is developed and a ...

Throughout, all rings are associative with an identity element but not necessarily commutative. During the decade of 1980s, a series of papers appeared in the Canadian Journal of Mathematics [1, 2] that had investigated pairs of commutative rings with the same set of prime ideals. In this paper, we consider some generalizations of that study in the noncommutative setting. Consider the ring R= H...

The prime and primitive spectra of Oq(k), the multiparameter quantized coordinate ring of affine n-space over an algebraically closed field k, are shown to be topological quotients of the corresponding classical spectra, specO(kn) and maxO(kn) ≈ kn, provided the multiplicative group generated by the entries of q avoids −1.

RESULTS ON N-ABSORBING IDEALS OF COMMUTATIVE RINGS by Alison Elaine Becker The University of Wisconsin-Milwaukee, 2015 Under the Supervision of Dr. Allen Bell Let R be a commutative ring with 1 6= 0. In his paper On 2-absorbing ideals of commutative rings, Ayman Badawi introduces a generalization of prime ideals called 2-absorbing ideals, and this idea is further generalized in a paper by Ander...

In this paper we study irreducible representations of regular limit subalgebras of AF-algebras. The main result is twofold: every closed prime ideal of a limit of direct sums of nest algebras (NSAF) is primitive, and every prime regular limit algebra is primitive. A key step is that the quotient of a NSAF algebra by any closed ideal has an AF C*-envelope, and this algebra is exhibited as a quot...

In this paper, for a complete lattice L, we introduce interval-valued L-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. Some characterization and properties are discussed.

We develop the theory of rational ideals for arbitrary associative algebras R without assuming the standard finiteness conditions, noetherianness or the Goldie property. The Amitsur-Martindale ring of quotients replaces the classical ring of quotients which underlies the previous definition of rational ideals but is not available in a general setting. Our main result concerns rational actions o...

in this paper, for a complete lattice l, we introduce interval-valued l-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. some characterization and properties are discussed.

The main result of this paper states that if R is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of R is a principal right ideal ring then R is right hereditary. In [10, Theorem 8] it is proved that if R is a right bounded prime ring of finite right Goldie dimension such that every proper homomorphic image is a...