Geodesic
Commutative feebly invo-clean group rings
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 61 (2019), pp. 5-10
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A commutative ring $R$ is called feebly invo-clean if any its element is of the form $\nu+e-f$, where $\nu$ is an involution and $e$, $f$ are idempotents. For every commutative unital ring $R$ and every abelian group $G$ we find a necessary and sufficient condition only in terms of $R$, $G$ and their sections when the group ring $R[G]$ is feebly invo-clean. Our result improves two recent own achievements about commutative invo-clean and weakly invo-clean group rings, published in Univ. J. Math. & Math. Sci. (2018) and Ural Math. J. (2019), respectively.
Keywords: invo-clean rings, weakly invo-clean rings, feebly invo-clean rings, group rings. 
@article{VTGU_2019_61_a0,
     author = {P. V. Danchev},
     title = {Commutative feebly invo-clean group rings},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--10},
     year = {2019},
     number = {61},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2019_61_a0/}
}
TY  - JOUR
AU  - P. V. Danchev
TI  - Commutative feebly invo-clean group rings
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2019
SP  - 5
EP  - 10
IS  - 61
UR  - http://geodesic.mathdoc.fr/item/VTGU_2019_61_a0/
LA  - en
ID  - VTGU_2019_61_a0
ER  - 
%0 Journal Article
%A P. V. Danchev
%T Commutative feebly invo-clean group rings
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2019
%P 5-10
%N 61
%U http://geodesic.mathdoc.fr/item/VTGU_2019_61_a0/
%G en
%F VTGU_2019_61_a0
P. V. Danchev. Commutative feebly invo-clean group rings. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 61 (2019), pp. 5-10. http://geodesic.mathdoc.fr/item/VTGU_2019_61_a0/

[1] P. V. Danchev, “Invo-clean unital rings”, Commun. Korean Math. Soc., 32:1 (2017), 19–27 | DOI | MR | Zbl

[2] P. V. Danchev, “Weakly invo-clean unital rings”, Afr. Mat., 28:7–8 (2017), 1285–1295 | DOI | MR | Zbl

[3] P. V. Danchev, “Feebly invo-clean unital rings”, Ann. Univ. Sci. Budapest (Math.), 60 (2017), 85–91 | MR | Zbl

[4] P. V. Danchev, “Weakly semi-boolean unital rings”, JP J. Algebra, Numb. Th. Appl. 39(3), 2017, 261–276 | MR | Zbl

[5] P. V. Danchev, “(2018) Commutative invo-clean group rings”, Univ. J. Math. Math. Sci., 11:1, 1–6 | MR | Zbl

[6] P. V. Danchev, “Commutative weakly invo-clean group rings”, Ural Math. J., 5:1 (2019), 48–52 | DOI | MR

[7] P. V. Danchev, W. Wm. McGovern, “Commutative weakly nil clean unital rings”, J. Algebra, 425:5 (2015), 410–422 | DOI | MR | Zbl

[8] G. Karpilovsky, “The Jacobson radical of commutative group rings”, Arch. Math., 39 (1982), 428–430 | DOI | MR | Zbl

[9] C. P. Milies, S. K. Sehgal, An Introduction to Group Rings, v. 1, Springer Science and Business Media, 2002 | MR

[10] D. Passman, The Algebraic Structure of Group Rings, Dover Publications, 2011 | MR