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Insertion-of-Factors-Property with factors nilpotents

이양|한준철|성효진|정의윤
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2014.12|한국수학논문집 (Korean Journal of Mathematics)|제22권 제4호|pp. 611-619|DOI http://dx.doi.org/10.11568/kjm.2014.22.4.611

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참고문헌

키워드

IFP ringAbelian ringnilpotentidempotentINFP ring
주제분류수학

초록

We in this note study a ring theoretic property which unifies Armendariz and IFP. We call this new concept INFP. We first show that idempotents and nilpotents are connected by the Abelian ring property. Next the structure of INFP rings is studied in relation to several sorts of algebraic systems.

Abstract

We in this note study a ring theoretic property which unifies Armendariz and IFP. We call this new concept INFP. We first show that idempotents and nilpotents are connected by the Abelian ring property. Next the structure of INFP rings is studied in relation to several sorts of algebraic systems.

참고문헌 (16)

  1. R. Antoine, "Nilpotent elements and Armendariz rings", J. Algebra, 319, pp.3128~3140 (2008)
  2. E.P. Armendariz, "A note on extensions of Baer and P.P.-rings", J. Austral. Math. Soc, 18, pp.470~473 (1974)
  3. H.E. Bell, "Near-rings in which each element is a power of itself", Bull. Austral. Math. Soc, 2, pp.363~368 (1970)
  4. G.M. Bergman, "Coproducts and some universal ring constructions", Tran. Amer. Math. Soc, 200, pp.33~88 (1974)
  5. G.M. Bergman, "Modules over coproducts of rings", Trans. Amer. Math. Soc, 200, pp.1~32 (1974)
  6. K.R. Goodearl, "Von Neumann Regular Rings" (1979), Pitman
  7. C. Huh, "p.p. rings and generalized p.p. rings", J. Pure Appl. Algebra, 167, pp.37~52 (2002)
  8. C. Huh, "A. Smoktunowicz, Armendariz rings and semicommutative ring", Comm. Algebra, 30, pp.751~761 (2002)
  9. Young Cheol Jeon, "On weak Armendariz rings", 대한수학회보, 46(1), pp.135~146 (2009), 대한수학회
  10. D.W. Jung, "Nil-Armendariz rings and upper nil-radicals", Internat. J. Math. Comput, 22, pp.1250059~ (2012)
  11. N.K. Kim, "Armendariz rings and reduced rings", J. Algebra, 223, pp.477~488 (2000)
  12. N.K. Kim, "Extensions of reversible rings", J. Pure Appl. Algebra, 185, pp.207~223 (2003)
  13. G. Marks, "On 2-primal Ore extensions", Comm. Algebra, 29, pp.2113~2123 (2001)
  14. L. Motais de Narbonne, "Anneaux semi-commutatifs et unis riels anneaux dont les id aux principaux sont idempotents", Proceedings of the 106th National Congress of Learned Societies, pp.71~73 (1982), Bib. Nat., Paris
  15. M.B. Rege, "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci, 73, pp.14~17 (1997)
  16. G. Shin, "Prime ideals and sheaf representation of a pseudo symmetric ring", Trans. Amer. Math. Soc, 184, pp.43~60 (1973)

관련 논문AI추천

INSERTION-OF-FACTORS-PROPERTY ON NILPOTENT ELEMENTS이양, 백진언, 엄태현, 전영철, 진우영, 최지웅대한수학회 · 대한수학회보2012 · 제49권 제2호INSERTION-OF-FACTORS-PROPERTY WITH FACTORS MAXIMAL IDEALS이양, 류성주, 성효진, 윤상조, 정다운, Hai Lan Jin대한수학회 · 대한수학회지2015 · 제52권 제3호Insertion-of-Ideal-Factors-Property이양, 김정수, 김주희, 류성주, 백상하, 서대재, 이동건, 이성엽, 한정민영남수학회 · East Asian Mathematical Journal2014 · 제30권 제5호A remark on IFP rings이양, 김시환, 김정수, 김정현, 류성주, 박재형, 송민경, 엄태강, 이민정, 이창혁, 임효진, 정민준, 황수민강원경기수학회 · 한국수학논문집2013 · 제21권 제3호Insertion property of nonzero powers at zero products김동화대한수학회 · 대한수학회논문집2018 · 제33권 제2호On weak Armendariz idealsEbrahim Hashemi대한수학회 · 대한수학회논문집2008 · 제23권 제3호

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