Let A be a commutative ring and E a non-zero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussian. The possibility for R to be Bézout is also studied, but a response is only given in the case where pSpec(A) (a quotient space of Spec(A)) is totally disconnected. Trivial ring extensions which are fqp-rings are cha...

We show that the ring of modular forms with characters for even unimodular lattice signature (2,10) is generated by weights 4, 10, 12, 16, 18, 22, 24, 28, 30, 36, 42, and 252 one relation weight 504. The proof based on comparison orbifold quotient symmetric domain root stack coarse moduli space.

Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $ngeq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,yin R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.

The Cox construction presents a toric variety as quotient of affine space by torus. category coherent sheaves on the corresponding stack thus has an evident description invariants in modules over polynomial ring. Here we give mirror to this description, and particular, clean new proof symmetry for smooth stacks.

This file contains additional information relating to the article: “A Search for Solvable Weighing Matrices,” submitted to Journal of Combinatorial Mathematics and Combinatorial Computing Feb. 25, 2005. In that article, we describe a computer search for group-developed weighing matrices of order 60 and weight 25, which we abbreviate as W (60, 25). Generally speaking, we view weighing matrices a...

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...