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 $.
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(https://doi.org/10.1007/s41980-020-00429-y)
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Series in Higher Mathematics D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960.
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Year 2021,
Volume: 30 Issue: 30, 260 - 268, 17.07.2021
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.
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.