آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 447 |
| تعداد مقالات | 4,557 |
| تعداد مشاهده مقاله | 5,380,005 |
| تعداد دریافت فایل اصل مقاله | 3,580,083 |
Gorenstein $n$-weak injective and Gorenstein $n$-weak flat modules under excellent extensions | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 375-389 اصل مقاله (358.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.20075.1319 | ||
| نویسنده | ||
| Mostafa Amini* | ||
| Department of Mathematics, Faculty of Sciences, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| Let $R$ be an associative ring and let $n$ be a non-negative integer. In this paper, we consider $n$-super finitely presented, Gorenstein $n$-weak injective and Gorenstein $n$-weak flat modules under change of rings. For an excellent extension $S\geq R$, we show that the Gorenstein $n$-super finitely presented dimensions (resp. weak Gorenstein $n$-super finitely presented dimensions) of rings $R$ and $S$ coincide. | ||
| کلیدواژه‌ها | ||
| almost excellent extension؛ excellent extension؛ Gorenstein $n$-weak injective module؛ Gorenstein $n$-weak flat module؛ $n$-super finitely presented module | ||
| مراجع | ||
|
[1] M . Amini , H . Amzil and D . Bennis , Category of modules n -weak injective and n -weak flat with respect to special super presented modules , Commun. Algebra 49, no. 11 (2021) 4924- 4939.
[2] M . Amini , H . Amzil and D . Bennis , Relative Gorenstein n-weak injective and n-weak flat modules , Commun . Algebra 51 , no. 1 (2023 ) 298- 313.
[3] Z . Gao and Z . Huang , Weak injective covers and dimension of modules , Acta Math . Hungar 147, (2015) 135-157 .
[4] Z . Gao and F . Wang , All Gorenstein hereditary rings are coherent , J . Algebra Appl 13, no . 04 (2014) 1350140 (5 pages).
[5] Z . Gao and F . Wang , Weak injective and weak flat modules , Commun . Algebra 43 , no . 9 (2015) 3857-3868.
[6] J . R . García Rozas and B . Torrecillas , Relative injective covers , Commun . Algebra 22 , no . 8 (1994) 2925-2940 .
[7] Z . Huang , Proper resolutions and Gorenstein categories , J . Algebra 393, (2013) 142-169 .
[8] H . K . Ng , Finitely presented dimension of commutative rings and modules , Pacific Journal of Mathematics 113, (1984) 417-431.
[9] J . Rotman , An Introduction to Homological Algebra , Second edition , Universitext , Springer , New York , (2009).
[10] W . Ren , Flat model structures under excellent extensions , Quaest. Math 43 , no. 8 (2020 ) 1173-1183.
[11] C . Selvaraj and P . Prabakaran , On n-Weak Cotorsion Modules , Lobachevskii . J . Math 39, (2018) 1428-1436 .
[12] W . Xu , On n-presented modules and almost excellent extensions , Commun . Algebra 27, no . 3 (1999) 1091-1102 .
[13] T . Zhao , Homological properties of modules with finite weak injective and weak flat dimensions , Int . Bull . Malays . Math . Sci . Soc 41, no . 2 (2018) 779-805 .
[14] T . Zhao and Y . Xu , Remarks on Gorenstein weak injective and weak flat modules , Alg . Colloq 27, no . 04 (2020) 687-702 .
[15] D . Zhou , On n-Coherent Rings and (n, d)-Rings , Commun . Algebra 32, n o . 6 (2004) 2425-2441 .
[16] Z . Zhu , On n-coherent rings , n-hereditary rings and n-regular rings , Bull . Iranian Math . Soc 37, no . 4 (2011) 251-267 . | ||
|
آمار تعداد مشاهده مقاله: 163 تعداد دریافت فایل اصل مقاله: 203 |
||