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 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 کاملA Graphical Characterization for SPAP-Rings
Let $R$ be a commutative ring and $I$ an ideal of $R$. The zero-divisor graph of $R$ with respect to $I$, denoted by $Gamma_I(R)$, is the simple graph whose vertex set is ${x in Rsetminus I mid xy in I$, for some $y in Rsetminus I}$, with two distinct vertices $x$ and $y$ are adjacent if and only if $xy in I$. In this paper, we state a relation between zero-divisor graph of $R$ with respec...
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...
متن کاملAutomorphisms of Perfect Power Series Rings
Let R be a perfect ring of characteristic p. We show that the group of continuous R-linear automorphisms of the perfect power series ring over R is generated by the automorphisms of the ordinary power series ring together with Frobenius; this answers a question of Jared Weinstein.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1970
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1970.33.79