Some Identities in Quotient Rings

被引：1

作者：

EL Hamdaoui, Mohammadi ^{[1
]}

Boua, Abdelkarim ^{[1
]}

Sandhu, Gurninder S. ^{[2
]}

机构：

[1] Sidi Mohammed Ben Abdellah Univ, Polydisciplinary Fac, Dept Math, LSI, Taza, Morocco

[2] Patel Mem Natl Coll, Dept Math, Rajpura, India

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2023年 / 41卷

关键词：

Generalized derivation; prime ideal; semi-prime ring; COMMUTATIVITY;

D O I：

10.5269/bspm.62481

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be an associative ring, P a prime ideal of R. In this paper, we study the structure of the ring R/P and describe the possible forms of the generalized derivations satisfying certain algebraic identities on R. As a consequence of our theorems, we first investigate strong commutativity preserving generalized derivations of prime rings, and then examine the generalized derivations acting as (anti)homomorphisms in prime rings. Some commutativity theorems are also given in prime rings.

引用

页码：19 / 19

页数：1

共 12 条

[1]

Ashraf M., 2002, Results Math., V42, P3, DOI DOI 10.1007/BF03323547

[2]

Beidar K.I., 1996, Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Mathematics

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

BELL, HE ;

DAIF, MN .

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

[4] SEMIDERIVATIONS OF PRIME-RINGS [J].

BRESAR, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 108 (04) :859-860

[5] COMMUTATIVITY WITH ALGEBRAIC IDENTITIES INVOLVING PRIME IDEALS [J].

El Mir, Hajar ;

Mamouni, Abdellah ;

Oukhtite, Lahcen .

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 35 (03) :723-731

[6] Herstein's theorem for prime ideals in rings with involution involving pair of derivations [J].

Khan, Mohammad Salahuddin ;

Ali, Shakir ;

Ayedh, Mohammed .

COMMUNICATIONS IN ALGEBRA, 2022, 50 (06) :2592-2603

[7]

LEE PH, 1983, B I MATH ACAD SIN, V11, P75

[8] On derivations involving prime ideals and commutativity in rings [J].

Mamouni, A. ;

Oukhtite, L. ;

Zerra, M. .

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2020, 14 (02) :675-688

[9]

Rehman N., 2004, Glas. Mat., V39, P27

[10] A NOTE ON MULTIPLICATIVE (GENERALIZED) (α, β)-DERIVATIONS IN PRIME RINGS [J].

Rehman, Nadeem Ur ;

Al-omary, Radwan M. ;

Muthana, Najat Mohammed .

ANNALES MATHEMATICAE SILESIANAE, 2019, 33 (01) :266-275

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