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PRIME RADICALS IN UP-MONOID RINGS

김진아|천정수
대한수학회 (The Korean Mathematical Society)|2012.05|대한수학회보 (Bulletin of the KMS)|제49권 제3호|pp. 511-515

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참고문헌

키워드

reduced ringupper nilradicallower nilradical(semi)prime ringup-monoid ring
주제분류수학

초록

We first show that the semiprimeness, primeness, and reducedness can go up to up-monoid rings. By these results we can compute the lower nilradicals of up-monoid rings, from which the well-known fact of Amitsur and McCoy for the polynomial rings can be extended to up-monoid rings.

Abstract

We first show that the semiprimeness, primeness, and reducedness can go up to up-monoid rings. By these results we can compute the lower nilradicals of up-monoid rings, from which the well-known fact of Amitsur and McCoy for the polynomial rings can be extended to up-monoid rings.

참고문헌 (8)

  1. V. Camillo, "Nilpotent ideals in polynomial and power series rings", Proc. Amer. Math. Soc, 138(5), pp.1607~1619 (2010)
  2. 홍찬용, "EXTENSIONS OF McCOY'S THEOREM", GLASGOW MATHEMATICAL JOURNAL, 52(0), pp.155~159, CAMBRIDGE UNIV PRESS
  3. E. Jespersa, "On radicals of graded rings", Comm. Algebra, 10, pp.1849~1854 (1982)
  4. T. Y. Lam, "A First Course in Noncommutative Rings" (1991), Springer-Verlag
  5. J. Lambek, "On the representations of modules by sheaves of factor modules", Canad. Math. Bull, 14, pp.359~368 (1971)
  6. J. Okninski, "Semigroup Algebras" (1991), Marcel Dekker
  7. D. S. Passman, "The Algebraic Structure of Group Rings" (1977), Wiley
  8. A. Smoktunowicz, "Polynomial rings over nil rings need not be nil", J. Algebra, 233(2), pp.427~436 (2000)

관련 논문AI추천

Armendariz property over prime radicals이양, 김홍기, 한준철대한수학회 · 대한수학회지2013 · 제50권 제5호Ring structures concerning factorization modulo radicals이양, 김홍기, Hai Lan Jin대한수학회 · 대한수학회보2017 · 제54권 제4호On a ring property related to nilradicals윤상조, Hai Lan Jin, Zhelin Piao강원경기수학회 · 한국수학논문집2019 · 제27권 제1호Reversibility over prime radicals이양, 성효진, 정다운강원경기수학회 · 한국수학논문집2014 · 제22권 제2호On n-Amitsur RingsBaatar Ochirbat, Deolinda I. C. Mendes, Sodnomkhorloo Tumurbat경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제4호ON A GENERALIZATION OF THE MCCOY CONDITION이양, 곽태근, 김남균, 김홍기, 여동은, 전영철대한수학회 · 대한수학회지2010 · 제47권 제6호

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