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STRONGLY GRADED RINGS WHICH ARE KRULL RINGS

Year 2019, , 120 - 128, 08.01.2019
https://doi.org/10.24330/ieja.504135

Abstract

Let $R = \oplus_{n \in \Z} R_{n}$ be a strongly graded ring of type $\Z$ and $R_{0}$ is a prime Goldie ring. It is shown that the following three conditions are equivalent: (i) $R_{0}$ is a $\Z$-invariant Krull ring, (ii) $R$ is a Krull ring and (iii) $R$ is a graded Krull ring. We completely describe all $v$-invertible $R$-ideals in $Q$, where $Q$ is a quotient ring of $R$.
 

References

  • E. Akalan, H. Marubayashi and A. Ueda, Generalized hereditary Noetherian prime rings, J. Algebra Appl., 17(8) (2018), 1850153 (22 pp).
  • H. Marubayashi, E. Nauwelaerts and F. Van Oystaeyen, Graded rings over arithmetical orders, Comm. Algebra, 12(5-6) (1984), 745-775.
  • H. Marubayashi and F. Van Oystaeyen, Prime Divisors and Noncommutative Valuation Theory, Lecture Notes in Mathematics, 2059, Springer, Heidelberg, 2012.
  • H. Marubayashi, S. Wahyuni, I. E. Wijayanti and I. Ernanto, Strongly graded rings which are maximal orders, Sci. Math. Jpn., 31 (2018), 2018-5.
  • C. Nastasescu and F.Van Oystaeyen, Graded Ring Theory, North-Holland Mathematical Library, 28, North-Holland Publishing Co., Amsterdam-New York, 1982.
  • B. Stenstrom, Rings of Quotients, An introduction to methods of ring theory, 217, Springer-Verlag, New York-Heidelberg, 1975.
  • F. Van Oystaeyen and A. Verschoren, Relative Invariants of Rings, The commutative theory, Monographs and Textbooks in Pure and Applied Mathematics, 79, Marcel Dekker, Inc., New York, 1983.
  • S. Wahyuni, H. Marubayashi, I. Ernanto and Sutopo, Strongly graded rings which are generalized Asano rings, preprint.
Year 2019, , 120 - 128, 08.01.2019
https://doi.org/10.24330/ieja.504135

Abstract

References

  • E. Akalan, H. Marubayashi and A. Ueda, Generalized hereditary Noetherian prime rings, J. Algebra Appl., 17(8) (2018), 1850153 (22 pp).
  • H. Marubayashi, E. Nauwelaerts and F. Van Oystaeyen, Graded rings over arithmetical orders, Comm. Algebra, 12(5-6) (1984), 745-775.
  • H. Marubayashi and F. Van Oystaeyen, Prime Divisors and Noncommutative Valuation Theory, Lecture Notes in Mathematics, 2059, Springer, Heidelberg, 2012.
  • H. Marubayashi, S. Wahyuni, I. E. Wijayanti and I. Ernanto, Strongly graded rings which are maximal orders, Sci. Math. Jpn., 31 (2018), 2018-5.
  • C. Nastasescu and F.Van Oystaeyen, Graded Ring Theory, North-Holland Mathematical Library, 28, North-Holland Publishing Co., Amsterdam-New York, 1982.
  • B. Stenstrom, Rings of Quotients, An introduction to methods of ring theory, 217, Springer-Verlag, New York-Heidelberg, 1975.
  • F. Van Oystaeyen and A. Verschoren, Relative Invariants of Rings, The commutative theory, Monographs and Textbooks in Pure and Applied Mathematics, 79, Marcel Dekker, Inc., New York, 1983.
  • S. Wahyuni, H. Marubayashi, I. Ernanto and Sutopo, Strongly graded rings which are generalized Asano rings, preprint.
There are 8 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İndah Emilia Wijayanti This is me

Hidetoshi Marubayashi This is me

İwan Ernanto This is me

Akira Ueda This is me

Publication Date January 8, 2019
Published in Issue Year 2019

Cite

APA Wijayanti, İ. E., Marubayashi, H., Ernanto, İ., Ueda, A. (2019). STRONGLY GRADED RINGS WHICH ARE KRULL RINGS. International Electronic Journal of Algebra, 25(25), 120-128. https://doi.org/10.24330/ieja.504135
AMA Wijayanti İE, Marubayashi H, Ernanto İ, Ueda A. STRONGLY GRADED RINGS WHICH ARE KRULL RINGS. IEJA. January 2019;25(25):120-128. doi:10.24330/ieja.504135
Chicago Wijayanti, İndah Emilia, Hidetoshi Marubayashi, İwan Ernanto, and Akira Ueda. “STRONGLY GRADED RINGS WHICH ARE KRULL RINGS”. International Electronic Journal of Algebra 25, no. 25 (January 2019): 120-28. https://doi.org/10.24330/ieja.504135.
EndNote Wijayanti İE, Marubayashi H, Ernanto İ, Ueda A (January 1, 2019) STRONGLY GRADED RINGS WHICH ARE KRULL RINGS. International Electronic Journal of Algebra 25 25 120–128.
IEEE İ. E. Wijayanti, H. Marubayashi, İ. Ernanto, and A. Ueda, “STRONGLY GRADED RINGS WHICH ARE KRULL RINGS”, IEJA, vol. 25, no. 25, pp. 120–128, 2019, doi: 10.24330/ieja.504135.
ISNAD Wijayanti, İndah Emilia et al. “STRONGLY GRADED RINGS WHICH ARE KRULL RINGS”. International Electronic Journal of Algebra 25/25 (January 2019), 120-128. https://doi.org/10.24330/ieja.504135.
JAMA Wijayanti İE, Marubayashi H, Ernanto İ, Ueda A. STRONGLY GRADED RINGS WHICH ARE KRULL RINGS. IEJA. 2019;25:120–128.
MLA Wijayanti, İndah Emilia et al. “STRONGLY GRADED RINGS WHICH ARE KRULL RINGS”. International Electronic Journal of Algebra, vol. 25, no. 25, 2019, pp. 120-8, doi:10.24330/ieja.504135.
Vancouver Wijayanti İE, Marubayashi H, Ernanto İ, Ueda A. STRONGLY GRADED RINGS WHICH ARE KRULL RINGS. IEJA. 2019;25(25):120-8.