COMMUTATIVE WEAKLY INVO–CLEAN GROUP RINGS
Abstract
A ring R is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring R and each abelian group G, we find only in terms of R, G and their sections a necessary and sufficient condition when the group ring R[G] is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings.
Keywords
Full Text:
PDFReferences
Danchev P.V. Invo-clean unital rings. Commun. Korean Math. Soc., 2017. Vol. 32, No. 1. P. 19–27. DOI: 10.4134/CKMS.c160054
Danchev P.V. Weakly invo-clean unital rings. Afr. Mat., 2017. Vol. 28, No. 7–8. P. 1285–1295. DOI: 10.1007/s13370-017-0515-7
Danchev P.V. Feebly invo-clean unital rings. Ann. Univ. Sci. Budapest (Math.), 2017. Vol. 60. P. 85–91.
Danchev P.V. Weakly semi-boolean unital rings. JP J. Algebra Number Theory Appl., 2017. Vol. 39, No. 3. P. 261–276. DOI: 10.17654/NT039030261
Danchev P.V. Commutative invo-clean group rings. Univ. J. Math. Math. Sci., 2018. Vol. 11, No. 1.P. 1–6. DOI: 10.17654/UM011010001
Danchev P.V., McGovern W.Wm. Commutative weakly nil clean unital rings. J. Algebra, 2015. Vol. 425, No. 5. P. 410–422. DOI: 10.1016/j.jalgebra.2014.12.003
Karpilovsky G. The Jacobson radical of commutative group rings. Arch. Math., 1982. Vol. 39, No. 5. P. 428–430. DOI: 10.1007/BF01899543
McGovern W.Wm., Raja Sh., Sharp A. Commutative nil clean group rings. J. Algebra Appl., 2015. Vol. 14, No. 6, art. no. 1550094. DOI: 10.1142/S0219498815500942
Milies C.P., Sehgal S.K. An Introduction to Group Rings. Netherlands: Springer, 2002. 371 p.
Passman D.S. The Algebraic Structure of Group Rings. Dover Publications, 2011. 752 p.
Article Metrics
Refbacks
- There are currently no refbacks.