منابع مشابه
Gaussian trivial ring extensions and fqp-rings
Let A be a commutative ring and E a non-zero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussian. The possibility for R to be Bézout is also studied, but a response is only given in the case where pSpec(A) (a quotient space of Spec(A)) is totally disconnected. Trivial ring extensions which are fqp-rings are cha...
متن کاملTrivial Extensions of Local Rings and a Conjecture of Costa
This paper partly settles a conjecture of Costa on (n, d)-rings, i.e., rings in which n-presented modules have projective dimension at most d. For this purpose, a theorem studies the transfer of the (n, d)-property to trivial extensions of local rings by their residue fields. It concludes with a brief discussion -backed by original examplesof the scopes and limits of our results. ∗This project ...
متن کاملOn derivations and biderivations of trivial extensions and triangular matrix rings
Triangular matrix rings are examples of trivial extensions. In this article we determine the structure of derivations and biderivations of the trivial extensions, and thereby we describe the derivations and biderivations of the upper triangular matrix rings. Some related results are also obtained.
متن کاملGeneralizations of Morphic Group Rings
An element a in a ring R is called left morphic if there exists b ∈ R such that 1R(a)= Rb and 1R(b)= Ra. R is called left morphic if every element ofR is left morphic. An element a in a ring R is called left π-morphic (resp., left G-morphic) if there exists a positive integer n such that an (resp., an with an = 0) is left morphic. R is called left π-morphic (resp., left G-morphic) if every elem...
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 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: Glasgow Mathematical Journal
سال: 2005
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089504002125