논문KCI 등재
Invo-clean unital rings
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초록
We define and completely describe the structure of invo-clean rings having identity. We show that these rings are clean but not (weakly) nil-clean and thus they possess independent properties than these obtained by Diesl in \cite{Di} and by Breaz-Danchev-Zhou in \cite{BDZ}.
Abstract
We define and completely describe the structure of invo-clean rings having identity. We show that these rings are clean but not (weakly) nil-clean and thus they possess independent properties than these obtained by Diesl in \cite{Di} and by Breaz-Danchev-Zhou in \cite{BDZ}.
참고문헌 (11)
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- S. Breaz, "Rings in which every element is either a sum or a difference of a nilpotent and an idempotent", J. Algebra Appl, 15(6), pp.11~ (2016)
- A. Cˆımpean, "Weakly nil-clean index and uniquely weakly nil-clean rings", Internat. Electr. J. Algebra, 21 (2017)
- P. V. Danchev, "Weakly UU rings", Tsukuba J. Math, 40, pp.101~118 (2016)
- P. V. Danchev, "Rings with unipotent units", Publ. Math. (Debrecen), 88, pp.449~466 (2016)
- P. V. Danchev, "Commutative weakly nil clean unital rings", J. Algebra, 425, pp.410~422 (2015)
- A. J. Diesl, "Nil clean rings", J. Algebra, 383, pp.197~211 (2013)
- N. Jacobson, "Structure theory for algebraic algebras of bounded degree", Ann. of Math, 46, pp.695~707 (1945)
- W. K. Nicholson, "Lifting idempotents and exchange rings", Trans. Amer. Math. Soc, 229, pp.269~278 (1977)
- W. K. Nicholson, "Rings in which elements are uniquely the sum of an idempotent and a unit", Glasg. Math. J, 46(2), pp.227~236 (2004)
- J. ˇ Ster, "Nil-clean involutions", arXiv preprint, ~ (2015)
관련 논문AI추천
Nil-clean rings of nilpotency index at most two with application to involution-clean ringsGuoli Xia, Xiaoshan Quan, Yu Li대한수학회 · 대한수학회논문집2018 · 제33권 제3호On $g(x)$-invo clean ringsHakima Mouanis, Mourad El Maalmi대한수학회 · 대한수학회논문집2020 · 제35권 제2호Singular clean ringsAfsaneh Nejadzadeh, Afshin Amini, Babak Amini, Habib Sharif대한수학회 · 대한수학회지2018 · 제55권 제5호Strongly clean matrix rings over noncommutative local ringsLi Bingjun대한수학회 · 대한수학회보2009 · 제46권 제1호FEEBLY NIL-CLEAN UNITAL RINGSPeter V. Danchev장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제1호Strong J-cleanness of formal matrix ringsA. Harmanci, O. Gurgun, S. Halicioglu장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제4호
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