منابع مشابه
On generalizations of semiperfect and perfect rings
We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel, that is, every simple right $R$-module has a flat $B$-cover. We give some properties of such rings along with examples. We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfe...
متن کاملModular Representations of Loewy Length Two
LetG be a finite p-group,K a field of characteristic p, and J the radical of the group algebra K[G]. We study modular representations using some new results of the theory of extensions of modules. More precisely, we describe the K[G]-modules M such that J2M = 0 and give some properties and isomorphism invariants which allow us to compute the number of isomorphism classes of K[G]-modulesM such t...
متن کاملTHE LOEWY LENGTH OF THE DESCENT ALGEBRA OF D2m+1.
In this article the Loewy length of the descent algebra of D2m+1 is shown to be m + 2, for m ≥ 2, by providing an upper bound that agrees with the lower bound in [Bonnafé and Pfeiffer, 2006]. The bound is obtained by showing that the length of the longest path in the quiver of the descent algebra of D2m+1 is at most m+1. To achieve this bound, the geometric approach to the descent algebra is us...
متن کاملon generalizations of semiperfect and perfect rings
we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel, that is, every simple right $r$-module has a flat $b$-cover. we give some properties of such rings along with examples. we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...
متن کاملPerfect Closures of Rings and Schemes1
0. In [3], Serre has defined the notion of a perfect variety over a field of characteristic p>0. Of course, a perfect variety is, in general, not a variety. The appropriate setting is that of schemes [2]. We show how to construct the perfect closure of a scheme, in particular, of a ring A, of characteristic p. This amounts to showing that the functor 5—>Ylom(A, B) is representable in the catego...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0276259-2