The cancellation problem for projective modules and related topics

1979 ◽  
pp. 323-338 ◽  
Author(s):  
A. A. Suslin
Keyword(s):  
Projective Modules ◽  
Cancellation Problem

scholarly journals Cancellation problem for projective modules over affine algebras

2008 ◽  
Vol 3 (3) ◽  
pp. 561-581 ◽  
Author(s):  
Manoj Kumar Keshari
Keyword(s):  
Monic Polynomial ◽  
Regular Sequence ◽  
Closed Field ◽  
Projective Modules ◽  
Affine Algebra ◽  
Algebraically Closed Field ◽  
Cancellation Problem ◽  
Affine Algebras ◽  
Open Question

AbstractLet A be an affine algebra of dimension n over an algebraically closed field k with 1/n! ∈ k. Let P be a projective A-module of rank n − 1. Then, it is an open question due to N. Mohan Kumar, whether P is cancellative. We prove the following results:(i) If A = R[T,T−1], then P is cancellative.(ii) If A = R[T,1/f] or A = R[T,f1/f,…,fr/f], where f(T) is a monic polynomial and f,f1,…,fr is R[T]-regular sequence, then An−1 is cancellative. Further, if k = p, then P is cancellative.

Invariance of projective modules in $$\mathsf {Sup}$$ under self-duality

2021 ◽  
Vol 82 (1) ◽  
Author(s):  
Javier Gutiérrez García ◽  
Ulrich Höhle ◽  
Tomasz Kubiak
Keyword(s):  
Projective Modules ◽  
Self Duality

scholarly journals Supplement submodules and a generalization of projective modules

2004 ◽  
Vol 277 (2) ◽  
pp. 689-702 ◽  
Author(s):  
M.C. Izurdiaga
Keyword(s):  
Projective Modules

scholarly journals Projective modules and prime submodules

2006 ◽  
Vol 56 (2) ◽  
pp. 601-611 ◽  
Author(s):  
Mustafa Alkan ◽  
Yücel Tiraş
Keyword(s):  
Projective Modules ◽  
Prime Submodules

Noncommutative G-semihereditary rings

2018 ◽  
Vol 17 (01) ◽  
pp. 1850014 ◽  
Author(s):  
Jian Wang ◽  
Yunxia Li ◽  
Jiangsheng Hu
Keyword(s):  
Associative Ring ◽  
Sufficient Condition ◽  
Projective Modules ◽  
The Third ◽  
Flat Modules ◽  
Gorenstein Projective Modules ◽  
Direct Limits ◽  
Gorenstein Flat ◽  
Finitely Presented ◽  
Semihereditary Rings

In this paper, we introduce and study left (right) [Formula: see text]-semihereditary rings over any associative ring, and these rings are exactly [Formula: see text]-semihereditary rings defined by Mahdou and Tamekkante provided that [Formula: see text] is a commutative ring. Some new characterizations of left [Formula: see text]-semihereditary rings are given. Applications go in three directions. The first is to give a sufficient condition when a finitely presented right [Formula: see text]-module is Gorenstein flat if and only if it is Gorenstein projective provided that [Formula: see text] is left coherent. The second is to investigate the relationships between Gorenstein flat modules and direct limits of finitely presented Gorenstein projective modules. The third is to obtain some new characterizations of semihereditary rings, [Formula: see text]-[Formula: see text] rings and [Formula: see text] rings.

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