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RISS 인기검색어
- 검색키워드
- 저자 : A. Cigdem Ozcan (검색결과 4 건)
- 무료
- 기관 내 무료
- 유료
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ON JACOBSON AND NIL RADICALS RELATED TO POLYNOMIAL RINGS
Kwak, Tai Keun,Lee, Yang,Ozcan, A. Cigdem Korean Mathematical Society 2016 대한수학회지 Vol.53 No.2
This note is concerned with examining nilradicals and Jacobson radicals of polynomial rings when related factor rings are Armendariz. Especially we elaborate upon a well-known structural property of Armendariz rings, bringing into focus the Armendariz property of factor rings by Jacobson radicals. We show that J(R[x]) = J(R)[x] if and only if J(R) is nil when a given ring R is Armendariz, where J(A) means the Jacobson radical of a ring A. A ring will be called feckly Armendariz if the factor ring by the Jacobson radical is an Armendariz ring. It is shown that the polynomial ring over an Armendariz ring is feckly Armendariz, in spite of Armendariz rings being not feckly Armendariz in general. It is also shown that the feckly Armendariz property does not go up to polynomial rings.
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On Jacobson and nil radicals related to polynomial rings
곽태근,이양,A. Cigdem Ozcan 대한수학회 2016 대한수학회지 Vol.53 No.2
This note is concerned with examining nilradicals and Jacobson radicals of polynomial rings when related factor rings are Armendariz. Especially we elaborate upon a well-known structural property of Armendariz rings, bringing into focus the Armendariz property of factor rings by Jacobson radicals. We show that $J(R[x])=J(R)[x]$ if and only if $J(R)$ is nil when a given ring $R$ is Armendariz, where $J(A)$ means the Jacobson radical of a ring $A$. A ring will be called {\it feckly Armendariz} if the factor ring by the Jacobson radical is an Armendariz ring. It is shown that the polynomial ring over an Armendariz ring is feckly Armendariz, in spite of Armendariz rings being not feckly Armendariz in general. It is also shown that the feckly Armendariz property does not go up to polynomial rings.
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Pinar Aydogdu,이양,A. Cigdem Ozcan 대한수학회 2012 대한수학회지 Vol.49 No.3
A ring R is called semiregular if R/J is regular and idem-potents lift modulo J, where J denotes the Jacobson radical of R. We give some characterizations of rings R such that idempotents lift modulo J, and R=J satises one of the following conditions: (one-sided) unit-regular, strongly regular, (unit, strongly, weakly) π-regular.
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Aydogdu, Pinar,Lee, Yang,Ozcan, A. Cigdem Korean Mathematical Society 2012 대한수학회지 Vol.49 No.3
A ring $R$ is called semiregular if $R/J$ is regular and idem-potents lift modulo $J$, where $J$ denotes the Jacobson radical of $R$. We give some characterizations of rings $R$ such that idempotents lift modulo $J$, and $R/J$ satisfies one of the following conditions: (one-sided) unit-regular, strongly regular, (unit, strongly, weakly) ${\pi}$-regular.
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