본문 바로가기
KERD
논문KCI 등재

On potent rings

Bingjun Li
대한수학회 (The Korean Mathematical Society)|2008.04|대한수학회논문집 (Communications of the KMS)|제23권 제2호|pp. 161-167

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Jacobson radicalidempotentspotent ringsformal power series ring.
주제분류수학

초록

A ring R is called an I0-ring if each left ideal not contained inthe Jacobson radical J(R) contains a non-zero idempotent. If, in addition,idempotents can be lifted modulo J(R),R is called an I -ring or a potentring. We study whether these properties are inherited by some relatedrings. Also, we investigate the structure of potent rings.

Abstract

A ring R is called an I0-ring if each left ideal not contained inthe Jacobson radical J(R) contains a non-zero idempotent. If, in addition,idempotents can be lifted modulo J(R),R is called an I -ring or a potentring. We study whether these properties are inherited by some relatedrings. Also, we investigate the structure of potent rings.

참고문헌 (11)

  1. G. Azumaya, "Strongly ¼-regular ring", J. Fac. Sci. Hokkaido Univ, 13, pp.34~39 (1954)
  2. V. P. Camillo, "Exchange rings, units and idempotents", Comm. Alg, 22(12), pp.4737~4749 (1994)
  3. P. Crawley, "Refinements for infinite direct decomposition of algebraic systems", Pacific. Math, 14, pp.797~855 (1964)
  4. K. R. Goodearl, "von Neuman Regular Rings" (1979), Pitman
  5. C. Y. Hong, "Exchange rings and their extensions", J. Pure and Appl. Alg, 179, pp.117~126 (2003)
  6. T. Y. Lam, "A First Course in Noncommutative Rings" (1991), Springer-Verlag
  7. W. K. Nicholson, "I-rings", Trans. Amer. Math. Soc, 207, pp.361~373 (1975)
  8. W. K. Nicholson, "Lifting idempotents and exchange rings", Trans. Amer. Math. Soc, 299, pp.269~278 (1977)
  9. J. Stock, "On rings whose projective modules have exchange property", J. Alg, 103, pp.437~453 (1986)
  10. R. B. Jr. Warfield, "Exchange rings and deposition modules", Math. Ann, 199, pp.31~36 (1992)
  11. H. P. Yu, "On the structure of exchange rings", Comm. Alg, 25(2), pp.661~670 (1997)

관련 논문AI추천

Rings close to semiregular이양, A. Cigdem Ozcan, Pinar Aydogdu대한수학회 · 대한수학회지2012 · 제49권 제3호On idempotents in relation with regularity이양, 박상원, 성효진, 윤상조, 한준철대한수학회 · 대한수학회지2016 · 제53권 제1호On weakly left quasi-commutative rings김동화, 윤상조, Zhelin Piao대한수학회 · 대한수학회논문집2017 · 제32권 제3호Nilpotent-duo property on powers김동화대한수학회 · 대한수학회논문집2018 · 제33권 제4호Rings in which every element is a sum of a nilpotent and three tripotentsGuoli Xia, Jian Cui대한수학회 · 대한수학회보2021 · 제58권 제1호ON A GENERALIZATION OF UNIT REGULAR RINGSTahire Ozen대한수학회 · 대한수학회보2023 · 제60권 제6호

이 간행물의 다른 논문 (15건)

Notes on a non-associative algebras with exponential functions III최설희pp. 153-159TOPOLOGICAL PROPERTIES IN BCC-ALGEBRAS안선신, 권석환pp. 169-178A note on lacunary statistically convergent double sequences of fuzzy numbersYavuz Altinpp. 179-185A reducibility of Exton's triple hypergeometric series X₂Arjun K. Rathie, 최준상pp. 187-189Solution of a vector variable bi-additive functional equation배재형, 박원길pp. 191-199
원문 보기