On trivial extensions which are quasi-Frobenius ones
نویسندگان
چکیده
منابع مشابه
Are Biseparable Extensions Frobenius?
In Secion 1 we describe what is known of the extent to which a separable extension of unital associative rings is a Frobenius extension. A problem of this kind is suggested by asking if three algebraic axioms for finite Jones index subfactors are dependent. In Section 2 the problem in the title is formulated in terms of separable bimodules. In Section 3 we specialize the problem to ring extensi...
متن کاملGraded self-injective algebras “are” trivial extensions
Article history: Received 20 March 2009 Available online 9 June 2009 Communicated by Michel Van den Bergh Dedicated to Professor Helmut Lenzing on the occasion of his seventieth birthday
متن کاملTraditional aging theories: which ones are useful?
Many theories have been proposed for answering two questions on aging: “Why do we age?” and “How do we age?” Among them, evolutionary theories are made for interpreting the evolutionary advantage of aging, and “saving resources for group benefit” is thought to be the purpose of aging. However for saving resources, a more economic strategy should be to make the individuals over reproduction age ...
متن کاملThe $w$-FF property in trivial extensions
Let $D$ be an integral domain with quotient field $K$, $E$ be a $K$-vector space, $R = D propto E$ be the trivial extension of $D$ by $E$, and $w$ be the so-called $w$-operation. In this paper, we show that $R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and in this case, each $w$-flat $w$-ideal of $R$ is $w$-invertible.
متن کاملA Note on Quasi-Frobenius Rings
The Faith-Menal conjecture says that every strongly right Johns ring is QF . The conjecture is also equivalent to say every right noetherian left FP -injective ring is QF . In this short article, we show that the conjecture is true under the condition( a proper generalization of left CS condition) that every nonzero complement left ideal is not small( a left ideal I is called small if for every...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tsukuba Journal of Mathematics
سال: 1982
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1496159450