Jacobson introduced the concept of K-rings, continuing the investigation of Kaplansky and Herstein into the commutativity of rings. In this note we focus on the ring-theoretic properties of K-rings. We first construct basic examples of K-rings to be handled easily. It is shown that a semiprime K-ring of bounded index of nilpotency is a commutative domain. It is proved that if R is a prime K-rin...

In this paper the notion of fuzzy ideals of a Γ-near-ring with respect to a t-norm is introduced and investigated some related properties. This concept of T -fuzzy ideals of a Γ-near-ring is a generalization of the concept of T -fuzzy ideals in near-rings. Also the notions of T -fuzzy ideals of a Γ-near-ring, quotient Γ-near-ring with respect to a t-norm and the sum of T -fuzzy ideals of a Γ-ne...

Let C be a smooth projective curve over the complex number field C. We investigate the structure of the cohomology ring of the quot schemes Quot(r, n), i.e., the moduli scheme of the quotient sheaves of O r C with length n. We obtain a filtration on H(Quot(r, n)), whose associated graded ring has a quite simple structure. As a corollary, we obtain a small generator of the ring. We also obtain a...

Let S be a cancellative monoid with quotient group of torsion-free rank a. We show that the monoid ring R[S] is a Hilbert ring if and only if the polynomial ring R[{ X, },s/] is a Hilbert ring, where |/| = a. Assume that R is a commutative unitary ring and G is an abelian group. The first research problem listed in [K, Chapter 7] is that of determining equivalent conditions in order that the gr...

1. Introduction. We shall say that an integral domain1 R satisfies condition (M) if any two nonzero elements of R have a nonzero common right multiple. In this note it is proved that if 5 is an extension of a ring R such that S is, roughly speaking, a noncommutative polynomial ring in one variable with R as a coefficient ring, and if R has the property (M), then 5 has property (M). In case R is...

The skein algebra of an oriented three-manifold is a classical limit the Kauffman bracket module and gives coordinate ring [Formula: see text]-character variety. In this paper, we determine quotient polynomial which isomorphic to group with three generators two relators. As application, give explicit formula for Borromean rings complement in text].

Let R be a polynomial ring in r variables over an infinite field K, and denote by D a corresponding dual ring, upon which R acts as differential operators. We study type two graded level Artinian algebras A = R/I , having socle degree j. For each such algebra A, we consider the family of Artinian Gorenstein [AG] quotients of A having the same socle degree. By Macaulay duality, A corresponds to ...

We give a proof using so-called fusion rings and q-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ring Gr(O(∞)). This is obtained here as a limiting case for analogous quotient maps for fusion categories, with the level going to ∞. This in turn allows a detailed description of the quotient map in terms of a re...

In this paper, we propose a weak version of quotient for the algebraic action group on variety, which shall call pseudo-quotient. They arise when focus purely topological properties good Geometric Invariant Theory (GIT) quotients regardless their properties. The flexibility granted by nature enables an easier identification in geometric constructions than classical GIT quotients. We obtain seve...