ON IF-RINGS

被引：0

作者：

Diompy, Mankagna Albert ^{[1
]}

Diabang, Andre Souleye ^{[2
]}

Diouf, Remy Diaga ^{[1
]}

Bousso, Ousseynou ^{[1
]}

机构：

[1] Univ Cheikh Anta Diop, Fac Sci & Tech, Dept Math Informat, Dakar, Senegal

[2] Univ Iba Der Thiam, Fac Sci & Tech, Dept Math & Informat, Thies, Senegal

来源：

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2024年 / 63卷 / 01期

关键词：

strongly cohopfian module; IF-ring; artinian ring with principal ideals; semilocal ring; quasi-Frobenius ring; Kothe ring; MODULES;

D O I：

10.17654/0972555524004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R denote an associative ring with unit 1 not equal 0. Then it is well known that any artinian R-module is strongly cohopfian, but the converse is not true, in general. The aim of this work is to study some classes of rings R for which strongly cohopfian modules and artinian modules coincide. These kinds of rings are said to be IF -rings. We characterize the IF -rings which are artinian principal ideals, the IFrings semilocal, the quasi-Frobenius IF -rings and the Kothe IF -rings.

引用

页码：65 / 76

页数：12

共 50 条

[21] On Π- coherence of rings
Zhu Zhanmin
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2017, 46 (05): : 875 - 886
[22] ON SEMILOCAL RINGS
Zhang, Hongbo
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (03) : 845 - 852
[23] On Clean Rings
Zhang, Hongbo
Camillo, Victor
COMMUNICATIONS IN ALGEBRA, 2016, 44 (06) : 2475 - 2481
[24] On τ-coherent rings
Masaike, Kanzo
RING THEORY 2007, PROCEEDINGS, 2009, : 240 - 247
[25] Factorizations of elements in local rings and semilocal rings of finite type
Arroyo Paniagua, Maria Jose
Facchini, Alberto
Tolooei, Yaser
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (12)
[26] Polynomial rings over commutative reduced Hopfian local rings
Dhorajia, A. M.
Mukherjee, H.
ACTA MATHEMATICA HUNGARICA, 2018, 154 (01) : 243 - 251
[27] Abelian groups whose endomorphism rings are V-rings
Amini, Afshin
Amini, Babak
Momtahan, Ehsan
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024,
[28] Local rings of bounded module type are almost maximal valuation rings
Couchot, F
COMMUNICATIONS IN ALGEBRA, 2005, 33 (08) : 2851 - 2855
[29] Zaks' conjecture on rings with semi-regular proper homomorphic images
Adarbeh, K.
Kabbaj, S.
JOURNAL OF ALGEBRA, 2016, 466 : 169 - 183
[30] The MacWilliams extending property and pseudo-Frobenius rings with essential socles
Quynh, Truong Cong
Kosan, M. Tamer
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2025,

← 1 2 3 4 5 →