Separative cancellation for projective modules over exchange rings
A separative ring is one whose finitely generated projective modules satisfy the property A⊕
A⋟ A⊕ B⋟ B⊕ B⇒ A⋟ B. This condition is shown to provide a key to a number of …
A⋟ A⊕ B⋟ B⊕ B⇒ A⋟ B. This condition is shown to provide a key to a number of …
Extensions of exchange rings
P Ara - Journal of Algebra, 1997 - Elsevier
We define non-unital exchange rings and we prove that ifIis an ideal of a ringR, thenRis an
exchange ring if and only ifIandR/Iare exchange rings and idempotents can be lifted …
exchange ring if and only ifIandR/Iare exchange rings and idempotents can be lifted …
Semiregular, weakly regular, and π-regular rings
AA Tuganbaev - Journal of Mathematical Sciences, 2002 - Springer
All rings are assumed to be associative and (except for nil-rings and for some stipulated
cases) to have nonzero identity elements. A ring A is said to be regular if for every element a …
cases) to have nonzero identity elements. A ring A is said to be regular if for every element a …
On Exchange QB∞-Rings
H Chen - Algebra Colloquium, 2007 - World Scientific
In this paper, we introduce a new class of rings, the QB∞-rings. We investigate necessary
and sufficient conditions under which an exchange ring is a QB∞-ring. The modules over an …
and sufficient conditions under which an exchange ring is a QB∞-ring. The modules over an …
On the stable range condition of exchange rings
T Wu, Y Xu - Communications in Algebra, 1997 - Taylor & Francis
The purpose of this paper is to prove the following facts: An exchange ring R has stable
range at most n if and only if for any module isomorphism Rn⊕ A≅ R⊕ B, A is isomorphic to …
range at most n if and only if for any module isomorphism Rn⊕ A≅ R⊕ B, A is isomorphic to …
Rings and modules with exchange properties
AA Tuganbaev - Journal of Mathematical Sciences, 2002 - Springer
A ring A is an exchange ring if the following two equivalent conditions hold:(1) for any
element a∈ A, there exists an idempotent e∈ aA with 1− e∈(1− a) A;(2) for any element a∈ …
element a∈ A, there exists an idempotent e∈ aA with 1− e∈(1− a) A;(2) for any element a∈ …
On exchange rings with primitive factor rings Artinian
C Huh, NK Kim, Y Lee - Communications in Algebra, 2000 - Taylor & Francis
On exchange rings with primitive factor rings artinian Page 1 COMMUNICATIONS IN
ALGEBRA, 28(10), 49894993 (2000) ON EXCHANGE RINGS WITH PRIMITIVE FACTOR …
ALGEBRA, 28(10), 49894993 (2000) ON EXCHANGE RINGS WITH PRIMITIVE FACTOR …
[PDF][PDF] On finitely generated projective modules and exchange rings
TS Wu, PW Chen - Algebra Colloquium, 2002 - researchgate.net
In this paper, we study interplay between exchange ring R and their J-semisimple
indecomposable factor rings. In particular, we prove that for any (exchange) ring R and any …
indecomposable factor rings. In particular, we prove that for any (exchange) ring R and any …
K 0 of Exchange Rings with All Idempotents Central
H Chen - Communications in Algebra®, 2005 - Taylor & Francis
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Exchange rings with general aleph-nought-comparability
T Wu - 2001 - Taylor & Francis
In this paper, the exchange ring R with the (general) ℵ0-comparability is studied. A ring R is
said to satisfy the general ℵ0-comparability, if for any idempotent elements f, g∈ R, there …
said to satisfy the general ℵ0-comparability, if for any idempotent elements f, g∈ R, there …