Theorem. Let R be a Cohen-Macaulay ring (locally, always) 1 c R an ideal o f height at least 2, S the Rees ring of R with respect to I, and G = S /S I the associated graded ring. Assume that S and G are Cohen-Macaulay rings, and that S has a canonical module cos. Then G has a canonical module r and: (i) I f co s can be embedded into S such that cos (considered as an ideal now) is not contained ...

In this paper we attempt to find and investigate the most general class of posets which satisfy a properly generalized version of the Hofmann-Mislove theorem. For that purpose, we generalize and study some notions (like compactness, the Scott topology, Scott open filters, prime elements, the spectrum etc.), and adjust them for use in general posets instead of frames. Then we characterize the po...

In this paper we give a computation of the mass spectrum of mesons and baryons. By this computation we show that there is a consecutive numbering of the mass spectrum of mesons and baryons. We show that in this numbering many stable mesons and baryons are assigned with a prime

Klein forms are used to construct generators for the graded algebra of modular level 7. Dissection formulas series imply Ramanujan type congruences modulo powers 7 a family generating functions that subsume counting function 7-core partitions. The broad class arithmetic considered here enumerate colored partitions by weights determined parts method is prototype similar analysis and at other pri...

Let I⊆R=K[x1,…,xn] be a toric ideal, i.e., binomial prime ideal. We investigate when the ideal I can “split” into sum of two smaller ideals. For general I, we give sufficient condition for this splitting in terms integer matrix that defines I. When I=IG is finite simple graph G, additional splittings IG related to subgraphs G. there exists I=I1+I2 show some cases describe (multi-)graded Betti n...

We describe the prime and primitive spectra for quantized enveloping algebras at roots of 1 in characteristic zero in terms of the prime spectrum of the underlying enveloping algebra. Our methods come from the theory of Hopf algebra crossed products. For primitive ideals we obtain an analogue of Duflo’s Theorem, which says that every primitive ideal is the annihilator of a simple highest weight...

In the setting of the modal logic that characterizes modal refinement over modal transition systems, Boudol and Larsen showed that the formulae for which model checking can be reduced to preorder checking, that is, the characteristic formulae, are exactly the consistent and prime ones. This paper presents general, sufficient conditions guaranteeing that characteristic formulae are exactly the c...