Center-like Subsets in Semiprime Rings with Multiplicative Derivations

被引：0

作者：

Aljohani, Sarah Samah ^{[1
]}

Sogutcu, Emine Koc ^{[2
]}

Rehman, Nadeem Ur ^{[3
]}

机构：

[1] Prince Sultan Univ, Dept Math & Sci, Riyadh 11586, Saudi Arabia

[2] Sivas Cumhuriyet Univ, Fac Sci, Dept Math, TR-58140 Sivas, Turkiye

[3] Aligarh Muslim Univ, Dept Math, Aligarh 202002, India

来源：

AXIOMS | 2024年 / 13卷 / 07期

关键词：

center-like subset; prime ring; semiprime ring; ideal; derivation; multiplicative derivation; COMMUTATIVITY;

D O I：

10.3390/axioms13070448

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce center-like subsets Z degrees*(A,d),Z degrees**(A,d), where A is the ring and d is the multiplicative derivation. In the following, we take a new derivation for the center-like subsets existing in the literature and establish the relations between these sets. In addition to these new sets, the theorems are generalized as multiplicative derivations instead of the derivations found in previous studies. Additionally, different proofs are provided for different center-like sets. Finally, we enrich this article with examples demonstrating that the hypotheses we use are necessary.

引用

页数：13

共 15 条

[1]

Bell HE, 2016, B IRAN MATH SOC, V42, P873

[2] ON COMMUTATIVITY AND STRONG COMMUTATIVITY-PRESERVING MAPS [J].

BELL, HE ;

DAIF, MN .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1994, 37 (04) :443-447

[3]

Bell HE., 1992, Int. J. Math. Math. Sci, V15, P205, DOI DOI 10.1155/S0161171292000255

[4]

Bell HE, 2005, Trends in Theory of Rings and Modules, P11

[5]

CHACRON M, 1976, P AM MATH SOC, V59, P211

[6]

Daif M.N., 1991, Internat. J. Math. & Math. Sci., V14, P615, DOI DOI 10.1155/S0161171291000844

[7]

Giambruno A., 1978, Rend. Circ. Mat. Palermo, V27, P270, DOI [10.1007/BF02843938, DOI 10.1007/BF02843938]

[8] HYPERCENTER OF A RING [J].

HERSTEIN, IN .

JOURNAL OF ALGEBRA, 1975, 36 (01) :151-157

[9]

Herstein IN., 1979, CANAD MATH B, V22, P509, DOI DOI 10.4153/CMB-1979-066-2

[10] Center-like subsets in rings with derivations or endomorphisms [J].

Idrissi, M. A. ;

Oukhtite, L. ;

Muthana, N. .

COMMUNICATIONS IN ALGEBRA, 2019, 47 (09) :3794-3799

← 1 2 →