STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING

A. Karimi Mansoub; A Moussavi; M Habibi

doi:https://doi.org/10.24330/ieja.296324

Article Details

STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING

Authors:

A. Karimi Mansoub | A Moussavi | M Habibi

Publisher:

Abdullah HARMANCI

Main Topics:

Mathematics

Journal:

International Electronic Journal of Algebra 2017 Vol.21 Issue 21, pp.164-179

Document Type:

Article

Publication Date:

1/2017

Document Language:

Turkish

Document ID (Org No.):

2000718088

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.296324

Abstract:

 


Let R be an associative ring with an endomorphism σ and F ∪ {0}
the free monoid generated by U = {u1, . . . , ut} with 0 added, and M a factor
of F setting certain monomial in U to 0, enough so that, for some n, Mn = 0.
Then we can form the skew monoid ring R[M; σ]. An element of a ring R is
strongly clean if it is the sum of an idempotent and a unit that commute. In
this paper, we prove that P
g∈M rgg ∈ R[M; σ] is a strongly clean element, if
re or 1 − re is strongly π-regular in R. As a corollary, we deduce that if R is a
strongly π-regular ring, then the skew monoid ring R[M; σ] is strongly clean.
These rings is a new family of non-semiprime strongly clean skew monoid rings. 

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Article Details

STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING

Authors: A. Karimi Mansoub | A Moussavi | M Habibi

Publisher: Abdullah HARMANCI

Main Topics: Mathematics

Journal: International Electronic Journal of Algebra 2017 Vol.21 Issue 21, pp.164-179

Document Type: Article

Publication Date: 1/2017

Document Language: Turkish

Document ID (Org No.): 2000718088

Frequency: Monthly

eISSN: 1306-6048

pISSN: 1306-6048

DOI: https://doi.org/10.24330/ieja.296324

Issues

Authors:

A. Karimi Mansoub | A Moussavi | M Habibi

Publisher:

Abdullah HARMANCI

Main Topics:

Mathematics

Journal:

International Electronic Journal of Algebra 2017 Vol.21 Issue 21, pp.164-179

Document Type:

Article

Publication Date:

1/2017

Document Language:

Turkish

Document ID (Org No.):

2000718088

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.296324