scholarly journals Projective modules over R[X1,z.sfnc;,Xn],R a prufer domain

1980 ◽  
Vol 18 (2) ◽  
pp. 165-171 ◽  
Author(s):  
Yves Lequain ◽  
Aron Simis
Keyword(s):  
Projective Modules ◽  
Prüfer Domain

The Cancellation Property of Projective Modules

2006 ◽  
Vol 13 (04) ◽  
pp. 617-622 ◽  
Author(s):  
Hongbo Zhang ◽  
Wenting Tong
Keyword(s):  
Projective Modules ◽  
Finitely Generated ◽  
Prüfer Domain ◽  
Cancellation Property ◽  
Dedekind Domains

An R-module M is said to have the cancellation property provided that M⊕ B ≅ M⊕ C implies B ≅ C for any pair of R-modules B and C. We obtain a characterization of the cancellation property for projective R-modules. With this result, it is proved that Dedekind domains have the cancellation property; and if R is a Prüfer domain, then R⊕ B ≅ R⊕ C implies B ≅ C for any pair of finitely generated R-modules B and C.

Quasi-strongly Gorenstein projective modules

2019 ◽  
Vol 18 (10) ◽  
pp. 1950182
Author(s):  
Kui Hu ◽  
Fanggui Wang ◽  
Longyu Xu ◽  
Dechuan Zhou
Keyword(s):  
Dedekind Domain ◽  
Projective Modules ◽  
Finitely Generated ◽  
Prüfer Domain ◽  
Dedekind Domains ◽  
Gorenstein Projective Modules ◽  
Semihereditary Rings

In this paper, we introduce the class of quasi-strongly Gorenstein projective modules which is a particular subclass of the class of finitely generated Gorenstein projective modules. We also introduce and characterize quasi-strongly Gorenstein semihereditary rings. We call a quasi-strongly Gorenstein semihereditary domain a quasi-SG-Prüfer domain. A Noetherian quasi-SG-Prüfer domain is called a quasi-strongly Gorenstein Dedekind domain. Let [Formula: see text] be a field and [Formula: see text] be an indeterminate over [Formula: see text]. We prove that every ideal of the ring [Formula: see text] is strongly Gorenstein projective. We also show that every ideal of the ring [Formula: see text] (respectively, [Formula: see text]) is strongly Gorenstein projective. These domains are examples of quasi-strongly Gorenstein Dedekind domains.

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 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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