Some results on Nonnil-multiplication rings

被引：5
|
作者：
Dabbabi, Abdelamir [1 ]
Moulahi, Samir [2 ,3 ]
机构：
[1] Univ Monastir, Fac Sci Monastir, Monastir 5000, Tunisia
[2] Univ Carthage, Fac Sci Bizerte, LR21ES10, Carthage 7000, Tunisia
[3] Univ Sousse, Higher Inst Appl Sci & Technol Sousse, Sousse 4003, Tunisia
来源：
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2023年 / 64卷 / 03期
关键词：
Multiplication ideal (module); (almost); Prime nilradical; Idealization; IDEALS;
D O I：
10.1007/s13366-022-00654-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce the concept of Nonnil-multiplication ring that is related to the class of multiplication rings. A commutative and unitary ring R is said to be Nonnil-multiplication if every nonnil ideal I of R is a multiplication ideal. We prove some basic properties of Nonnil-multiplication rings and we use idealization construction to establish examples of Nonnil-multiplication rings that are not multiplication rings.
引用
收藏
页码：753 / 760
页数：8
相关论文
共 50 条
  • [21] Some results of multiplication modules
    Tavallaee, Hamid Agha
    Mahtabi, Robabeh
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2022, 15 (11)
  • [22] Maximal non-nonnil-principal ideal rings
    Kumar, Rahul
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024,
  • [23] Some results on Γ-rings
    Mukherjee, RN
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2003, 34 (06): : 991 - 994
  • [24] Nonnil-Noetherian Rings and Formal Power Series
    Benhissi, Ali
    ALGEBRA COLLOQUIUM, 2020, 27 (03) : 361 - 368
  • [25] DEFINING MULTIPLICATION IN SOME ADDITIVE EXPANSIONS OF POLYNOMIAL RINGS
    Point, Francoise
    Rigo, Michel
    Waxweiler, Laurent
    COMMUNICATIONS IN ALGEBRA, 2016, 44 (05) : 2075 - 2099
  • [26] SOME PROPERTIES OF NON-COMMUTATIVE MULTIPLICATION RINGS
    UKEGAWA, T
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1978, 54 (09) : 279 - 284
  • [27] On nonnil-very strong finite type commutative rings
    Dabbabi, Abdelamir
    Benhissi, Ali
    SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2024, 18 (01): : 111 - 120
  • [28] Multiplication rings and graded rings
    Escoriza, J
    Torrecillas, B
    COMMUNICATIONS IN ALGEBRA, 1999, 27 (12) : 6213 - 6232
  • [29] Some results of topological rings
    Manfe, Riyam K.
    Abed, Majid Mohammed
    JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2022, 25 (06) : 1869 - 1873
  • [30] Some Results of QF Rings
    Jun, Dong
    KYUNGPOOK MATHEMATICAL JOURNAL, 2009, 49 (03): : 451 - 456
12345