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A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS

Year 2021, Volume: 30 Issue: 30, 260 - 268, 17.07.2021
https://doi.org/10.24330/ieja.969924

Abstract

In this paper, we introduce and study $ \mathcal{H}_Y $-s.m.c. and strong $ \mathcal{H}_Y $-s.m.c. sets and give some connections between them and lattice ideals of $ \mathcal{H}_Y $. Also, we introduce an ideal $ R_S $, for each subset set $ S $ of a ring $ R $. We prove a ring $ R $ is a Gelfand ring if and only if $ R_S $ is an intersection of maximal ideals, for every s.m.c. set $ S $ of $ R $.

References

  • A. R. Aliabad, M. Badie and S. Nazari, An extension of $z$-ideals and $z^\circ$-ideals, Hacet. J. Math. Stat., 49(1) (2020), 254-272.
  • M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
  • F. Azarpanah, M. Ghirati and A. Taherifar, Closed ideals in $C(X)$ with different representations, Houston J. Math., 44(1) (2018), 363-383.
  • M. Badie, On $\mathcal{H}_Y$ -ideals, Bull. Iranian Math. Soc., (2020), to appear. (https://doi.org/10.1007/s41980-020-00429-y)
  • L. Gillman and M. Jerison, Rings of Continuous Functions, The University Series in Higher Mathematics D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960.
  • R. Y. Sharp, Steps in Commutative Algebra, Second edition, London Mathematical Society Student Texts, 51, Cambridge University Press, Cambridge, 2000.
  • S. A. Steinberg, Lattice-Ordered Rings and Modules, Dordrecht, Springer, 2010.
  • S. Willard, General Topology, Addison-Wesley Publishing Co., Reading, New York, 1970.
Year 2021, Volume: 30 Issue: 30, 260 - 268, 17.07.2021
https://doi.org/10.24330/ieja.969924

Abstract

References

  • A. R. Aliabad, M. Badie and S. Nazari, An extension of $z$-ideals and $z^\circ$-ideals, Hacet. J. Math. Stat., 49(1) (2020), 254-272.
  • M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
  • F. Azarpanah, M. Ghirati and A. Taherifar, Closed ideals in $C(X)$ with different representations, Houston J. Math., 44(1) (2018), 363-383.
  • M. Badie, On $\mathcal{H}_Y$ -ideals, Bull. Iranian Math. Soc., (2020), to appear. (https://doi.org/10.1007/s41980-020-00429-y)
  • L. Gillman and M. Jerison, Rings of Continuous Functions, The University Series in Higher Mathematics D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960.
  • R. Y. Sharp, Steps in Commutative Algebra, Second edition, London Mathematical Society Student Texts, 51, Cambridge University Press, Cambridge, 2000.
  • S. A. Steinberg, Lattice-Ordered Rings and Modules, Dordrecht, Springer, 2010.
  • S. Willard, General Topology, Addison-Wesley Publishing Co., Reading, New York, 1970.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehdi Badıe This is me

Publication Date July 17, 2021
Published in Issue Year 2021 Volume: 30 Issue: 30

Cite

APA Badıe, M. (2021). A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS. International Electronic Journal of Algebra, 30(30), 260-268. https://doi.org/10.24330/ieja.969924
AMA Badıe M. A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS. IEJA. July 2021;30(30):260-268. doi:10.24330/ieja.969924
Chicago Badıe, Mehdi. “A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS”. International Electronic Journal of Algebra 30, no. 30 (July 2021): 260-68. https://doi.org/10.24330/ieja.969924.
EndNote Badıe M (July 1, 2021) A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS. International Electronic Journal of Algebra 30 30 260–268.
IEEE M. Badıe, “A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS”, IEJA, vol. 30, no. 30, pp. 260–268, 2021, doi: 10.24330/ieja.969924.
ISNAD Badıe, Mehdi. “A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS”. International Electronic Journal of Algebra 30/30 (July 2021), 260-268. https://doi.org/10.24330/ieja.969924.
JAMA Badıe M. A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS. IEJA. 2021;30:260–268.
MLA Badıe, Mehdi. “A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS”. International Electronic Journal of Algebra, vol. 30, no. 30, 2021, pp. 260-8, doi:10.24330/ieja.969924.
Vancouver Badıe M. A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS. IEJA. 2021;30(30):260-8.