منابع مشابه
Commuting $pi$-regular rings
R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.
متن کاملCombining Local and Von Neumann Regular Rings
All rings R considered are commutative and have an identity element. Contessa called R a VNL-ring if a or 1 a has a Von Neumann inverse whenever a 2 R. Sample results: Every prime ideal of a VNL-ring is contained in a unique maximal ideal. Local and Von Neumann regular rings are VNL and if the product of two rings is VNL, then both are Von Neumann regular, or one is Von Neumann regular and the ...
متن کاملCOHEN-MACAULEY AND REGULAR LOCAL RINGS Contents
1. Flat, projective, and free modules 1 2. Review of regular local rings 2 3. Cohen-Macauley rings 2 4. The Koszul complex 3 5. The Koszul resolution detects depth 5 6. The detection of depth by use of Ext 6 7. Global dimension 6 8. Minimal resolutions and global dimension 7 9. Serre’s characterization of regular local rings 8 10. The Auslander-Buchsbaum theorem 10 11. Localizations of regular ...
متن کاملUnique Factorization in Regular Local Rings.
In this note we prove that every regular local ring of dimension 3 is a unique factorization domain. Nagata4 showed (Proposition 11) that if every regular local ring of dimension 3 is a unique factorization domain, then every regular local ring has unique factorization.* Thus, combining these results we have that every regular local ring is a unique factorization domain. Throughout this note R ...
متن کاملPeriodically Regular Chordal Rings
ÐChordal rings have been proposed in the past as networks that combine the simple routing framework of rings with the lower diameter, wider bisection, and higher resilience of other architectures. Virtually all proposed chordal ring networks are nodesymmetric, i.e., all nodes have the same in/out degree and interconnection pattern. Unfortunately, such regular chordal rings are not scalable. In ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1972
ISSN: 0002-9947
DOI: 10.2307/1996383