Cilt 21, Sayı 21, Sayfalar 164 - 179 2017-01-17

STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING

A. Karimi Mansoub [1] , A Moussavi [2] , M Habibi [3]

143 115

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. 

Skew monoid ring,strongly clean ring
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Konular Matematik ve İstatistik
Dergi Bölümü Makaleler
Yazarlar

Yazar: A. Karimi Mansoub
E-posta: arezoukarimimansoub@gmail.com

Yazar: A Moussavi
E-posta: moussavi.a@modares.ac.ir

Yazar: M Habibi
E-posta: mhabibi@tafreshu.ac.ir

Bibtex @araştırma makalesi { ieja296324, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {21}, pages = {164 - 179}, doi = {10.24330/ieja.296324}, title = {STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING}, language = {en}, key = {cite}, author = {Habibi, M and Mansoub, A. Karimi and Moussavi, A} }
APA Mansoub, A , Moussavi, A , Habibi, M . (2017). STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING. International Electronic Journal of Algebra, 21 (21), 164-179. DOI: 10.24330/ieja.296324
MLA Mansoub, A , Moussavi, A , Habibi, M . "STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING". International Electronic Journal of Algebra 21 (2017): 164-179 <http://dergipark.gov.tr/ieja/issue/27921/296324>
Chicago Mansoub, A , Moussavi, A , Habibi, M . "STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING". International Electronic Journal of Algebra 21 (2017): 164-179
RIS TY - JOUR T1 - STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING AU - A. Karimi Mansoub , A Moussavi , M Habibi Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.296324 DO - 10.24330/ieja.296324 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 164 EP - 179 VL - 21 IS - 21 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.296324 UR - http://dx.doi.org/10.24330/ieja.296324 Y2 - 2016 ER -
EndNote %0 International Electronic Journal of Algebra STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING %A A. Karimi Mansoub , A Moussavi , M Habibi %T STRONGLY CLEAN ELEMENTS OF A SKEW MONOID RING %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 21 %N 21 %R doi: 10.24330/ieja.296324 %U 10.24330/ieja.296324