Some characterizations of the maximal ZG-regular ideal in a ring

Farmani, Marzieh

doi:10.22098/jhs.2025.17344.1090

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	Some characterizations of the maximal ZG-regular ideal in a ring
Journal of Hyperstructures
دوره 14، شماره 2، اسفند 2025، صفحه 176-183 اصل مقاله (1.6 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22098/jhs.2025.17344.1090
نویسنده
Marzieh Farmani^*
Department of Mathematices, Islamic Azad University, Roudehen Branch, Roudehen, Tehran, Iran.
چکیده
Let R be an associative ring with identity. A ring R is called ZG-regular( resp. strongly ZG-regular) if, for every a in R, there exist positive integer n and g in G, such that a^ng ∈a^^ngRa^^ng (resp. a^^ng ∈a^^(n+1)gR. In this paper, we shall show that the join of all ZG-regular ideals in an arbitrary ring R is a ZG-regular ideal, and so there exists a unique maximal ZG-regular ideal M = M(R) in R, whose structure we investigate. Furthermore, we establish the necessary and sufficient condition for a ring to be a direct sum of its ideals.
کلیدواژه‌ها
group؛ ring؛ ZG-regular؛ strongly ZG-regular؛ maximal ZG-regular ideal

مراجع
[1] P. Ara, π-Regular rings have stable range one, Proc. Amer. Math. Soc., 124 (11) (1996), 3293-3298. [2] G. Azumaya, Strongly π-regular rings, J. Fac. Sci. Hokkaido Univ. 13 (1954), 34-39. MR. 16:788. [3] A. Badawi, Abelian π-regular rings, Comm. Algebra, 25 (4) (1997), 1009-1021. [4] A. Badawi, On semicommutative π-regular rings, Comm. Algebra, 22 (1) (1993), 151-157. [5] W. D. Burgess, P. Menal, Strongly π-regular rings and homomorphisms into them, Comm. Algebra, 16 (1988), 1701-1725. [6] R. Yue Chi Ming, On Von Neumann regular rings, III, Monat. Math., 86 (1978), 251-257. [7] A. Y. M. Chin and H. V. Chen, On strongly π-regular, Southeast Asian Bull. Math., 26 (2002), 387-390. [8] M. F. Dischinger, Sur les anneaux fortment π-reguliers, C. R. Acad. Sci. Paris, Ser. A 283 (1976), 571-573. [9] K. R. Goodearl, Von Neumann regular rings, Monographs and studied in Math. 4, Pitman, London, 1979. [10] T. Y. Lam, A first course in noncommutative rings, Second edition. Graduate Texts in Mathematics, 131. Springer-Verlag, New York, 2001. [11] Sh. Safari Sabet, Commuting regular rings, Int. J. Appl. Math., 14(4) (2003), 357-364. [12] Sh. Safari Sabet, M. Farmani, Extensions of regular rings, Int. J. Indus. Math., 8(4) (2016), 331-337.
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Some characterizations of the maximal ZG-regular ideal in a ring