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Locally divided domains of the form D[X]Nv

장규환
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2010.03|한국수학논문집 (Korean Journal of Mathematics)|제18권 제1호|pp. 37-43

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키워드

UMT-domain(t-)locally divided domainthe ring D[X]Nv
주제분류수학

초록

Let D be an integral domain, X be an indeterminate over D, and Nv = {f ∈ D[X]| (Af)v = D}. In this paper, we introduce the concept of t-locally divided domains, and we then prove that D[X]Nv is a locally divided domain if and only if D is a t-locally divided UMT-domain, if and only if D[X] is a t-locally divided domain.

Abstract

Let D be an integral domain, X be an indeterminate over D, and Nv = {f ∈ D[X]| (Af)v = D}. In this paper, we introduce the concept of t-locally divided domains, and we then prove that D[X]Nv is a locally divided domain if and only if D is a t-locally divided UMT-domain, if and only if D[X] is a t-locally divided domain.

참고문헌 (13)

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  6. D.E. Dobbs, "Divided rings and going-down", Pacific J. Math., 67, pp.353~363 (1976)
  7. D.E. Dobbs, "On locally divided integral domains and CPI-overrings", Internat. J. Math. Sci., 4, pp.119~135 (1981)
  8. D.E. Dobbs, "Locally pseudo-valuation domains", Ann. Mat. Pura Appl.(4), 134, pp.147~168 (1983)
  9. M. Fontana, "UMT-domains and domains with Prufer integral closure", Comm. Algebra, 26, pp.1017~1039 (1998)
  10. R. Gilmer, "Multiplicative Ideal Theory" (1972), Dekker
  11. J.R. Hedstrom, "Pseudo-valuation domains", Pacific J. Math., 75, pp.137~147 (1978)
  12. E. Houston, "On t-invertibility, II", Comm. Algebra, 17, pp.1955~1969 (1989)
  13. Nv, "J. Algebra", 1989, 151~170

관련 논문AI추천

LOCALLY PSEUDO-VALUATION DOMAINS OF THE FORM D[X]Nv장규환대한수학회 · 대한수학회지2008 · 제45권 제5호On almost pseudo-valuation domains, II장규환강원경기수학회 · 한국수학논문집2011 · 제19권 제4호A Note on S-Noetherian Domains임정욱경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호On almost pseudo-valuation domains장규환강원경기수학회 · 한국수학논문집2010 · 제18권 제2호t-SPLITTING SETS S OF AN INTEGRAL DOMAIN D SUCH THAT DS IS A FACTORIAL DOMAIN장규환강원경기수학회 · 한국수학논문집2013 · 제21권 제4호ON ALMOST FACTORIALITY OF INTEGRAL DOMAINS임정욱장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제4호

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