본문 바로가기
KERD
논문KCI 등재

Kaplansky-type Theorems, II

장규환|김환구
경북대학교 자연과학대학 수학과|2011.09|Kyungpook Mathematical Journal|제51권 제3호|pp. 339-344

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

prime (primary) elementKaplansky theoremupper to zero in D[X]
주제분류수학

초록

Let D be an integral domain with quotient field K, X be an indeterminate over D, and D[X] be the polynomial ring over D. A prime ideal Q of D[X] is called an upper to zero in D[X] if Q = fK[X] ∩ D[X] for some f ∈ D[X]. In this paper, we study integral domains D such that every upper to zero in D[X] contains a prime element (resp., a primary element, a t-invertible primary ideal, an invertible primary ideal).

Abstract

Let D be an integral domain with quotient field K, X be an indeterminate over D, and D[X] be the polynomial ring over D. A prime ideal Q of D[X] is called an upper to zero in D[X] if Q = fK[X] ∩ D[X] for some f ∈ D[X]. In this paper, we study integral domains D such that every upper to zero in D[X] contains a prime element (resp., a primary element, a t-invertible primary ideal, an invertible primary ideal).

참고문헌 (15)

  1. D. D. Anderson, "Quasi-Schreier domains, II", Comm. Algebra, 35, pp.2096~2104 (2007)
  2. D. D. Anderson, "Almost Bézout domains", J. Algebra, 142, pp.285~309 (1991)
  3. D. D. Anderson, "On a theorem of Kaplansky", Boll. Un. Mat. Ital. A, 8(7), pp.397~402 (1994)
  4. D. F. Anderson, "Almost splitting sets in integral domains II", J. Pure Appl. Algebra, 208, pp.351~359 (2007)
  5. D. F. Anderson, "Generalized weakly factorial domains", Houston J. Math, 29, pp.1~13 (2003)
  6. A. Bouvier, "Le groupe des classes d'un anneau intègre", 107ème Congres des Sociétés Savantes, Brest, pp.85~92 (1982)
  7. S. Gabelli, "On divisorial ideals in polynomial rings over Mori domains", Comm. Alge-bra, 15, pp.2349~2370 (1987)
  8. R. Gilmer, "Multiplicative Ideal Theory" (1972), Marcel Dekker
  9. E. Houston, "On t-invertibility, II", Comm. Algebra, 17, pp.1955~1969 (1989)
  10. Nv, "J. Algebra", 1989, 151~170
  11. 강병균, "ON THE CONVERSE OF A WELL-KNOWN FACT ABOUT KRULL DOMAINS", JOURNAL OF ALGEBRA, 124, pp.284~299
  12. I. Kaplansky, "Commutative Rings" (1974), Univ. of Chicago
  13. H. Kim, "Kaplansky-type theorems", Kyungpook Math. J, 40, pp.9~16 (2000)
  14. R. Lewin, "Almost generalized GCD-domains", Lecture Notes in Pure and Appl. Math, 189, pp.371~382 (1997), Marcel Dekker
  15. M. Zafrullah, "A general theory of almost factoriality", Manuscripta Math, 51, pp.29~62 (1985)

관련 논문AI추천

UPPERS TO ZERO IN POLYNOMIAL RINGS WHICH ARE MAXIMAL IDEALS장규환대한수학회 · 대한수학회보2015 · 제52권 제2호Almost splitting sets S of an integral domain D such that D_S is a PID장규환강원경기수학회 · 한국수학논문집2011 · 제19권 제2호On almost pseudo-valuation domains, II장규환강원경기수학회 · 한국수학논문집2011 · 제19권 제4호KAPLANSKY-TYPE THEOREMS IN GRADED INTEGRAL DOMAINS김환구, 오동렬, 장규환대한수학회 · 대한수학회보2015 · 제52권 제4호Locally divided domains of the form D[X]Nv장규환강원경기수학회 · 한국수학논문집2010 · 제18권 제1호Graded integral domains and Nagata rings, II장규환강원경기수학회 · 한국수학논문집2017 · 제25권 제2호

이 간행물의 다른 논문 (9건)

Coefficient Inequalities for Certain Subclasses of Analytic Functions De ned by Using a General Derivative OperatorSerap Bulutpp. 241-250Certain Class of Multidimensional Convolution Integral Equations Involving a Generalized Polynomial SetJamal Mohammed Shenan, Tariq Omar Salimpp. 251-260On Seifert Matrices of Symmetric Links배용주, 이인숙pp. 261-281On a Class of Semicommutative RingsTahire Özen, Abdullah Harmanci, Nazim Agayevpp. 283-291Path-Connectivity of Two-Interval MSF WaveletsDivya Singhpp. 293-300
원문 보기