We define the basis monomial ring M, of a matroid G and prove that it is Cohen-Macaulay for finite G. We then compute the Krull dimension of M, , which is the rank over Q of the basis-point incidence matrix of G, and prove that dim B, > dim M, under a certain hypothesis on coordinatizability of G, w
Rees cones and monomial rings of matroids
β Scribed by Rafael H. Villarreal
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 129 KB
- Volume
- 428
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
Right cones are semigroups with a left cancellation law such that for any two elements a, b there exists an element c with b s ac or a s bc. Valuation rings, cones of ordered or left ordered groups, semigroups of ordinal numbers, and Hjelmslev rings are examples. The ideal theory of these semigroups
By JAMES A. RATE and JOHN K . LUEDEMAN of Clemson (I7.S.A.) (Eingegangen am 22. 11. 1979) REES matrix semigroups &I= (S, ,I, -1, P) over a semigroup correspond loosely to the n X n matrix rings over it ring R. It is well known that &(R,)x .=(&(R)),,. Moreover, when S is it finite BRANDT semigroup, S