We investigate the Cohen-Macaulay property for rings of invariants under multiplicative actions of a finite group G. By definition, these are G-actions on Laurent polynomial algebras k[x 1 , . . . , x ±1 n ] that stabilize the multiplicative group consisting of all monomials in the variables xi. For the most part, we concentrate on the case where the base ring k is Z. Our main result states tha...

We characterize strong F-regularity, a property associated with tight closure, in a large class of rings. A special case of our results is a workable criterion in complete intersection rings. Tight closure is a recently introduced operation linked to a variety of results in commutative algebra. Among the major results achieved with its use are a generalization of the Direct Summand Conjecture f...

We extend the notion of face rings simplicial complexes and posets to case finite-length (possibly infinite) with a group action. The action on complex induces an ring, we prove that ring invariants is isomorphic quotient poset under mild condition action.We also identify class actions preserve homotopical Cohen–Macaulay property quotients. When acted-upon independence semimatroid, h-polynomial...

Let H ⊆ Z be a positive semigroup generated by A ⊆ H, and let K[H] be the associated semigroup ring over a field K. We investigate heredity of the Cohen–Macaulay property from K[H] to both its A -Newton graded ring and to its face rings. We show by example that neither one inherits in general the Cohen–Macaulay property. On the positive side we show that for every H there exist generating sets ...

This paper considers the problems of finite determinacy and approximation flat analytic maps from germs real (resp. complex) spaces to R </mml...

1 CONTENTS 1. Introduction 2. Molien's theorem 3. Cohen-Macaulay rings 4. Groups generated by pseudo-reflections 5. Three applications 6. Syzygies 7. The canonical module 8. Gorenstein rings 9. Complete intersections 10. Monomial groups 1. Introduction. The theory of invariants of finite groups forms an interesting and relatively self-contained nook in the imposing edifice of commuta-tive algeb...

The Auslander-Reiten conjecture is a notorious open problem about the vanishing of Ext modules. In Cohen-Macaulay complete local ring R with parameter ideal Q, holds for if and only it residue R/Q. former part this paper, we study R/Qℓ in connection that R, prove equivalence them case where Gorenstein ℓ≤dim⁡R. latter part, generalize result minimal multiplicity by J. Sally. Due to these two our...