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The rate of a graded moduleMover a standard graded algebraR,rateR(M), is a measure of the growth of the shifts in the minimal graded free resolution ofM. In this paper, we study the rate of Veronese modules ofM. More precisely, it is shown thatfor allc≥1. This extends a result of Aramova et al. [2] As a consequence of this, ifMis generated in degree zero, then, for allc≥max{rateR(M),Rate(R)}. Also, it is shown that, for all integerss,c≥1. In particular case, we give a simple proof to a result of Backelin. [ABSTRACT FROM PUBLISHER]

Let R be a commutative Noetherian ring. In this article, we provide some new criteria for a semidualizing module to be dualizing in terms of special homological properties of module categories. The purpose of this article is twofold: first, it aims at improving Christensen's and Takahashi et al.'s characterizations of dualizing modules; secondly, while applying these criteria to the ring itself, we not only recover some results of Jenda and Xu, respectively, but also obtain a new characterization of Gorenstein rings. [ABSTRACT FROM PUBLISHER]

Let k be an algebraically closed field of characteristic 0, and let A = k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e., a graded A-linear homomorphism ∇: Derk(A) → Endk(M), that satisfies the derivation property and preserves the Lie product. In particular, a torsion free module N over the complete local ring [image omitted] admits a natural integrable connection if A is a simple curve singularity, or if A is irreducible and N is a gradable module. [ABSTRACT FROM AUTHOR]

Recently Jain, López-Permouth and Syed classified indecomposable non-local right continuous right π-rings. In the present article we describe the structure of right continuous right π-rings. [ABSTRACT FROM AUTHOR]