For a radical monomial ideal I in a normal semigroup ring k[Q], there is a unique minimal irreducible resolution 0 → k[Q]/I → W 0 → W 1 → · · · by modules W i of the form ⊕ j k[Fij ], where the Fij are (not necessarily distinct) faces of Q. That is, W i is a direct sum of quotients of k[Q] by prime ideals. This paper characterizes Cohen–Macaulay quotients k[Q]/I as those whose minimal irreducib...

The content of a polynomial f(t) is the ideal generated by its coefficients. Our aim here is to consider a beautiful formula of Dedekind–Mertens on the content of the product of two polynomials, to explain some of its features from the point of view of Cohen–Macaulay algebras and to apply it to obtain some Noether normalizations of certain toric rings. Furthermore, the structure of the primary ...

We prove that the f -vector of members in a certain class of meet semi-lattices satisfies Macaulay inequalities 0 ≤ ∂k(fk) ≤ fk−1 for all k ≥ 0. We construct a large family of meet semi-lattices belonging to this class, which includes all posets of multicomplexes, as well as meet semi-lattices with the ”diamond property”, discussed by Wegner [11], as special cases. Specializing the proof to the...

This thesis is largely a consolidation of parts of lectures given by Yoshino, Y. at Tokyo Metropolitan University in 1987 (cf. [17]). We aim to investigate the Cohen-Macaulay modules of simple plane curve singularities. We consider such simple plane curve singularities algebraically as quotient rings R = k[[x, y]]/(f) of the formal power series ring in two variables over an algebraically closed...

We study rings of integral modular forms for congruence subgroups as modules over the ring full group. In many cases these are free or decompose at least into well-understood pieces. apply this to characterize which Cohen--Macaulay and prove finite generation results. These theorems based on decomposition results about vector bundles compactified moduli stack elliptic curves.

In this article, we introduce an invariant of Cohen-Macaulay local rings in terms the reduction number canonical ideals. The can be defined arbitrary and it measures how close to being Gorenstein. First, clarify relation between almost Gorenstein nearly by using dimension one. We next characterize idealization trace ideals over invariant. It provides better prospects for a result on property id...