Let M be a symplectic manifold, equipped with a Hamiltonian action of a torus T . We give an explicit formula for the rational cohomology ring of the symplectic quotient M//T in terms of the cohomology ring of M and fixed point data. Under some restrictions, our formulas apply to integral cohomology. In certain cases these methods enable us to show that the cohomology of the reduced space is to...

In this note we first show that for a right (resp. left) Ore ring R and an automorphism σ of R, if R is σ-skew McCoy then the classical right (resp. left) quotient ring Q(R) of R is σ̄-skew McCoy. This gives a positive answer to the question posed in Başer et al. [1]. We also characterize semiprime right Goldie (von Neumann regular) McCoy (σ-skew McCoy) rings.

Introduction Let B = k[x 1 ,. .. , x n ] be a polynomial ring over a field k and A = B/J a quotient ring of B by a homogeneous ideal J. Let m denote the maximal graded ideal of A. Then the Rees algebra R = A[mt] may be considered a standard graded k-algebra and has a presentation B[y 1 ,. In this paper we want to compare the ideals J and I J as well as their homological properties.

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertib...

Let $A$ be the quotient of a graded polynomial ring $\mathbb{Z}[x_1,\cdots,x_m]\otimes\Lambda[y_1,\cdots,y_n]$ by an ideal generated monomials with leading coefficients 1. Then we constructed space~$X_A$ such that is isomorphic to $H^*(X_A)$ modulo torsion elements.

We prove that in a ring Rwith an identity there exists an element a ∈ R and a nonzero derivation d ∈ Der R such that ad(a) 6= 0. A ring R is said to be a d-rigid ring for some derivation d ∈ Der R if d(a) = 0 or ad(a) 6= 0 for all a ∈ R. We study rings with rigid derivations and establish that a commutative Artinian ring R either has a non-rigid derivation or R = R1 ⊕ · · · ⊕ Rn is a ring direc...

The purpose of this short note is to prove that if R an alternative ring whose associators are not zero-divisors, then has no zero-divisors. By a result Bruck and Kleinfeld, if, in addition, the characteristic 2, central quotient octonion division algebra over some field.

We consider a Deligne–Mumford stack $X$ which is the quotient of an affine scheme $\operatorname {Spec}A$ by action finite group $G$ and show that Balmer spectrum tensor triangulated category perfect complexes on homeomorphic to space homogeneous prime ideals in cohomology ring $H^*(G,A)$ .

A weight ring in type A is the coordinate ring of the GIT quotient of the variety of flags in Cn modulo a twisted action of the maximal torus in SL(n, C). We show that any weight ring in type A is generated by elements of degree strictly less than the Krull dimension, which is at worst O(n). On the other hand, we show that the associated semigroup of Gelfand–Tsetlin patterns can have an essenti...

Let R be a commutative ring with identity and T (R) its total quotient ring. We extend the notion of well-centered overring of an integral domain to an arbitrary commutative ring and we investigate the transfer of this property to different extensions of commutative rings in both integral and non-integral cases. Namely in pullbacks and trivial extensions. Our aim is to provide new classes of co...