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...

Let k be a field of finite characteristic p, and G a finite group acting on the left on a finite dimensional k-vector space V . Then the dual vector space V ∗ is naturally a right kG-module, and the symmetric algebra of the dual, R := Sym(V ∗), is a polynomial ring over k on which G acts naturally by graded algebra automorphisms, and if k is algebraically closed can be regarded as the space k[V...

The homological property of the associated graded ring an ideal is important problem in commutative algebra and algebraic geometry. In this paper we explore almost Cohen–Macaulayness stretched $\mathfrak{m}$-primary ideals case where reduction number attains minimal value a Cohen–Macaulay local $(A,\mathfrak{m})$. As application, present complete descriptions with small number.

We study the coordinate ring of an $L$-convex polyomino, determine its regularity in terms maximal number rooks that can be placed polyomino. also characterize Gorenstein polyominoes and those which are on punctured spectrum, compute Cohen–Macaulay type any polyomino rectangles covering it. Though main results algebraic nature, all proofs combinatorial.

Let R be a local ring and C semidualizing module of R. We investigate the behavior certain classes generalized Cohen-Macaulay R-modules under Foxby equivalence between Auslander Bass with respect to C. In particular, we show that are invariant this if M is finitely generated R-module in class such C\otimes_RM surjective Buchsbaum, then also Buchsbaum.

R.G. and Perez proved that under certain conditions the test ideal of a module closure agrees with trace closure. We use this fact to compute ideals various rings respect closures coming from their indecomposable maximal Cohen–Macaulay modules. also give an easier way hypersurface ring in three variables particular type matrix factorization.

One of the main open questions in liaison theory is whether every homogeneous Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the G-liaison class of a complete intersection. We give an affirmative answer to this question for StanleyReisner ideals defined by simplicial complexes that are weakly vertex-decomposable. This class of complexes includes matroid, shifted and Goren...

We exhibit the elementary but somewhat surprising property that most direct links of prime ideals in Gorenstein rings are equimultiple ideals. It leads to the construction of a bountiful set of Cohen–Macaulay Rees algebras.

The rings of quantum integrals of the generalized Calogero-Moser systems related to the deformed root systems An(m) and Cn(m, l) with integer multiplicities and corresponding algebras of quasi-invariants are investigated. In particular, it is shown that these algebras are finitely generated and free as the modules over certain polynomial subalgebras (Cohen-Macaulay property). The proof follows ...