پیوندهای مفید
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 306 |
| تعداد مقالات | 2,645 |
| تعداد مشاهده مقاله | 3,966,287 |
| تعداد دریافت فایل اصل مقاله | 2,671,425 |
Generalizations of prime submodules over non-commutative rings | ||
| Journal of Hyperstructures | ||
| دوره 11، شماره 1، شهریور 2022، صفحه 65-83 اصل مقاله (334.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2528 | ||
| نویسنده | ||
| Emel Aslankarayigit Ugurlu* | ||
| Department of Mathematics, Marmara University, P.O.Box 34722, Istanbul, Turkey | ||
| چکیده | ||
| Throughout this paper, R is an associative ring (not necessarily commutative) with identity and M is a right R-module with unitary. In this paper, we introduce a new concept of ∅-prime submodule over an associative ring with identity. Thus we define the concept as following: Assume that S(M) is the set of all submodules of M and Ø : S(M) ! S(M) [ f;g is a function. For every Y 2 S(M) and ideal I of R; a proper submodule X of M is called Ø-prime, if YI ⊆ X and YI ⊄ Ø(X); then Y ⊆ X or I ⊆ (X :R M): Then we examine the properties of Ø-prime submodules and characterize it when M is a multiplication module. | ||
| کلیدواژه‌ها | ||
| $\phi-$prime Submodule؛ Non-commutative Ring؛ Multiplication Module | ||
| مراجع | ||
|
[1] R. Ameri, On the prime submodules of multiplication modules, Inter. J. Math. Math. Sci., 27 (2003), 1715-1724. [2] D. D. Anderson and M. Batanieh, Generalizations of prime ideals, Comm. Algebra, 36 (2008), 686-696. [3] D. D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math., 29 (2003) 831-840. [4] D. D. Anderson, Cancellation modules and related modules, Lect. Notes Pure Appl. Math., 220 (2001), 13-25. [5] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, SpringerVerlag, New York, (1992). [6] S. E. Atani and F. Farzalipour, On weakly prime submodules, Tamk. J. Math., 38 (3) (2007), 247-252. [7] M. F. Atiyah and I. G. MacDonald, Introduction to commutative algebra, CRC Press (1969). [8] P. K. Beiranvand and R. Beyranvand, Almost prime and weakly prime submodules, J. Algebra Appl., 18 (7) (2019), 1950129, 14 pp. [9] S. M. Bhatwadekar and P. K. Sharma, Unique factorization and birth of almost primes, Comm. Algebra, 33 (2005), 43-49. [10] J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181. [11] T. Y. Lam, A rst course in noncommutative rings, Second Edition, Springer, (1991). [12] C. P. Lu, Prime submodules of modules, Comm. Math. Univ. Sancti Pauli, 33 (1984), 61-69. [13] R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20 (1992), 1803-1817. [14] S. K. Nimbhorkar and J. A. Khubchandani, Fuzzy essential-small submodules and Fuzzy small-essential submodules, Journal of Hyperstructures, 9 (2), (2020), 52-67. [15] A. A. Tuganbaev, Multiplication modules, Journal of Mathematical Sciences, 123 (2) (2004), 3839-3905. [16] N. Zamani, Ø-prime submodules, Glasgow Math. J., 52 (2) (2010), 253-259. | ||
|
آمار تعداد مشاهده مقاله: 10 تعداد دریافت فایل اصل مقاله: 15 |
||