منابع مشابه
Picard Groups, Grothendieck Rings, and Burnside Rings of Categories
We discuss the Picard group, the Grothendieck ring, and the Burnside ring of a symmetric monoidal category, and we consider examples from algebra, homological algebra, topology, and algebraic geometry. In October, 1999, a small conference was held at the University of Chicago in honor of Saunders Mac Lane’s 90th birthday. I gave a talk there based on a paper that I happened to have started writ...
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Let K be a a global field and O be an order of K. We develop algorithms for the computation of the unit group of residue class rings for ideals in O. As an application we show how to compute the unit group and the Picard group of O provided that we are able to compute the unit group and class group of the maximal order e O of K.
متن کاملAuthentication schemes from actions on graphs, groups, or rings
We propose a couple of general ways of constructing authentication schemes from actions of a semigroup on a set, without exploiting any specific algebraic properties of the set acted upon. Then we give several concrete realizations of this general idea, and in particular, we describe several authentication schemes with long-term private keys where forgery (a.k.a. impersonation) is NP-hard. Comp...
متن کاملPicard-graded Betti Numbers and the Defining Ideals of Cox Rings
Different choices of basis yield (non-canonically) isomorphic Cox rings and any of them is a “total” coordinate ring for X in the sense that, (1) The homogeneous coordinate rings ⊕∞ s=0H (X, sD) of all images of X via complete linear systems φD : X → P(H(X,D)) are subalgebras of Cox(X). (2) If the Cox ring is a finitely generated k-algebra then X can be obtained as a quotient of an open set of ...
متن کاملGraded Cohen-macaulayness for Commutative Rings Graded by Arbitrary Abelian Groups
We consider a commutative ring R graded by an arbitrary abelian group G, and define the grade of a G-homogeneous ideal I on R in terms of vanishing of C̆ech cohomology. By defining the dimension in terms of chains of homogeneous prime ideals and supposing R satisfies a.c.c. on G-homogeneous ideals and has a unique G-homogeneous maximal ideal, we can define graded versions of the depth of R and C...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7862