Amalgamated rings with m-nil clean properties

Authors

DOI:

https://doi.org/10.23755/rm.v48i0.1133

Keywords:

Clean ring, nil-clean m-clean, m-nil clean, m-potent

Abstract

In this paper, we study the transfer of the notion of $m$-nil clean (i.e., a ring in which  every element is a sum of a nilpotent and  an $m$-potent elements) to the amalgamarted rings. We also find many sufficient and necessary conditions for the   $m$-nil clean property  to the amalgamated rings.

References

A. M. R. Barati and A. Abyzov. Rings whose elements are sums of m-potents and nilpotents. Commun. in Algebra, 50:4437–4459, 2022.

M. D’Anna and M. Fontana. The amalgamated duplication of a ring along a multiplicative-canonical ideal. Ark. Mat., 45:241–252, 2007a.

M. D’Anna and M. Fontana. An amalgamated duplication of a ring along an ideal: the basic properties. J. Algebra Appl., 6:443–459, 2007b.

A. Diesl. Nil clean rings. J. Algebra, 383:197–211, 2013.

N. M. M. Chhiti and M. Tamekkante. Clean property in amalgamated algebras along an ideal. Hacettepe J. Math. Stat., 44:41–49, 2015.

C. F. M. D’Anna and M. Fontana. Amalgamated algebras along an ideal. Commutative Algebra and its Applications, pages 155–172, 2009.

C. F. M. D’Anna and M. Fontana. Properties of chains of prime ideals in amalgamated algebras along an ideal. J. Pure Appl. Algebra, 214:1633–1641, 2010.

W. Nicholson. Lifting idempotents and exchange rings. Trans. Amer. Math. Soc., 229:269–278, 1977.

T. D. S. Purkait and S. Kar. On m-clean and strongly m-clean rings. Commun. Algebra, 48:218–227, 2020.

H. T. Y. Hirano and A.Yaqub. On rings in which every elements is uniquely expressible as a sum of nilpotent and certain potent lement. Math. J. Okayama Univ., 30:33–40, 1988.

Y. Ye. Semiclean rings. Commun. Algebra, 31, 2003.

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Published

2023-12-30

Issue

Section

Volume 48-2023