We show that any quasi-Gorenstein deformation of a 3-dimensional Buchsbaum local ring with I-invariant 1 admits maximal Cohen-Macaulay module, provided it is quotient Gorenstein ring. Such class rings includes two instances unique factorization domains constructed by Marcel-Schenzel and Imtiaz-Schenzel, respectively. Apart from this result, motivated the small conjecture in prime characteristic...

In this paper we focus on a special class of commutative local‎ ‎rings called SPAP-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎We characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an SPAP-ring and derive some basic properties‎. ‎Then we answer the‎ ‎question of Lam and Reyes about strongly Oka ideals fam...

The regularity part follows from the primary decompositions part, so the heart of this paper is the analysis of the primary decompositions. In [S], this was proved for the primary components of height at most one over the ideal. This paper proves the existence of such a k but does not provide a formula for it. In the paper [SS], Karen E. Smith and myself find explicit k for ordinary and Frobeni...

In §1 we use COO-vector methods, essentially Frobenius reciprocity, to derive the Howe-Richardson multiplicity formula for compact nilmanifolds. In §2 we use Frobenius reciprocity to generalize and considerably simplify a reduction procedure developed by Howe for solvable groups to general extensions of nilpotent Lie groups. In §3 we give an application of the previous results to obtain a reduc...

In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The construction was derived as modification of the well-known four circulant codes. Applying together with building-up construction, construct singly-even binary lengths 56, 58, 64, 80 and 92 that were not known in literature before. Singly-even length $\b...

We give a new proof of the well known Wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎We apply the concept of Frobenius kernel in Frobenius representation theorem in finite group‎ ‎theory to build a proof‎.