지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
오류제보하기
We observe from known results that the set of nilpotent elements inArmendariz rings has an important role. The upper nilradical coincides with the prime radical in Armendariz rings. So it can be shown that the factor ring of an Armendariz ring over its prime radical is also Armendariz, with the help of Antoine's results for nil-Armendariz rings. We study the structure of rings with such property in Armendariz rings and introduce APR as a generalization. It is shown that APR is placed between Armendariz and nil-Armendariz. It is shown that an APR ring which is not Armendariz, can always be constructed from any Armendariz ring. It is also proved that a ring R is APR if and only if so is R[x], and that N(R[x])=N(R)[x] when R is APR, where R[x] is the polynomial ring with an indeterminate x over R and N(-) denotes the set of all nilpotent elements. Several kinds of APR rings are found or constructed in the precess related to ordinary ring constructions.
목차
등록된 정보가 없습니다.
참고문헌 (29)
참고문헌 신청
C. Huh / 1998 / Questions on 2-primal rings / Comm. Algebra 26 (2) : 595 ~ 600
C. Huh / 2001 / Prime radicals of formal power series rings / Bull. Korean Math. Soc 38 (4) : 623 ~ 633
C. Huh / 2002 / Armendariz rings and semicommutative rings / Comm. Algebra 30 (2) : 751 ~ 761
C. Huh / 2002 / p.p. rings and generalized p.p. rings / J. Pure Appl. Algebra 167 (1) : 37 ~ 52
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 (7) : 2265 ~ 2272
C. Huh / 2001 / Prime radicals of formal power series rings / Bull. Korean Math. Soc 38 (4) : 623 ~ 633
C. Huh / 2002 / Armendariz rings and semicommutative rings / Comm. Algebra 30 (2) : 751 ~ 761
C. Huh / 2002 / p.p. rings and generalized p.p. rings / J. Pure Appl. Algebra 167 (1) : 37 ~ 52
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 (7) : 2265 ~ 2272
이 논문의 저자 정보
최근 본 자료
댓글(0)
0