Finite Complete Intersection Algebras and the Completeness Radical
โ Scribed by B. de Smit; H.W. Lenstra Jr.
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 207 KB
- Volume
- 196
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
โฆ Synopsis
Let A be a ring, and let B be a finite A-algebra. If B is of the form w x ลฝ . A X , . . . , X r f , . . . , f then we say that B is a complete intersection over A.
๐ SIMILAR VOLUMES
Let R be a monomial subalgebra of k x 1 x N generated by square free monomials of degree two. This paper addresses the following question: when is R a complete intersection? For such a k-algebra we can associate a graph G whose vertices are x 1 x N and whose edges are x i x j x i x j โ R . Convers
It is shown that the G-dimension and the complete intersection dimension are relative projective dimensions. Relative Auslander-Buchsbaum formulas are discussed. New cohomology theories, called complexity cohomology, are constructed. The new theories play the same role in identifying rings (and modu
trivial derivations of strictly negative degree. If moreover all the weights of the variables x are even it follows that the Serre spectral sequence of any orientable i fibration F ยจE ยช B, with H \*F s A as graded algebras, collapses at the E -term, 2 thus verifying a conjecture of Halperin. We also