scholarly journals Some Commutativity Theorems for Near-Rings with Left Multipliers

2020 ◽  
Vol 44 (2) ◽  
pp. 205-216
Author(s):  
A. BOUA ◽  
◽  
A. Y. ABDELWANIS ◽  
A. CHILLALI
Keyword(s):  
Commutativity Theorems

scholarly journals An iteration technique and commutativity of rings

1990 ◽  
Vol 13 (2) ◽  
pp. 315-319
Author(s):  
H. A. S. Abujabal ◽  
M. S. Khan
Keyword(s):  
Commutativity Theorems ◽  
Iteration Technique

Through much shorter proofs, some new commutativity theorems for rings with unity have been obtained. These results either extend or generalize a few well-known theorems. Our method of proof is based on an iteration technique.

scholarly journals A commutativity theorem for lefts-unital rings

1990 ◽  
Vol 13 (4) ◽  
pp. 769-774
Author(s):  
Hamza A. S. Abujabal
Keyword(s):  
Commutativity Theorem ◽  
Unital Ring ◽  
Commutativity Theorems ◽  
Associative Rings ◽  
Unital Rings

In this paper we generalize some well-known commutativity theorems for associative rings as follows: LetRbe a lefts-unital ring. If there exist nonnegative integersm>1,k≥0, andn≥0such that for anyx,yinR,[xky−xnym,x]=0, thenRis commutative.

scholarly journals ON COMMUTATIVITY OF ONE-SIDED $s$-UNITAL RINGS

1992 ◽  
Vol 23 (3) ◽  
pp. 253-268
Author(s):  
H. A. S. ABUJABAL ◽  
M. A. KHAN ◽  
M. S. SAMMAN
Keyword(s):  
Commutativity Theorems ◽  
Unital Rings

In the present paper, we study the commutativity of one sided s-unital rings satisfying conditions of the form $[x^r y\pm x^ny^mx^s,x]= 0 = [x^ry^m\pm x^ny^{m^2}x^s, x]$, or $[yx^r\pm x^ny^mx^s, x] = 0 = [y^mx^r\pm x^ny^{m^2}x^s, x]$ for each $x$,$y \in R$, where $m = m(y) > 1$ is an integer depending on $y$ and $n$, $r$ and $s$ are fixed non-negative integers. Other commutativity theorems are also obtained. Our results generalize·some of the well-known commutativity theorems for rings.

scholarly journals Commutativity theorems for groups and semigroups

2018 ◽  
Vol 74 (3) ◽  
pp. 243-255 ◽  
Author(s):  
Francisco Araújo ◽  
Michael Kinyon
Keyword(s):  
Commutativity Theorems

scholarly journals Commutativity theorems for rings with polynomial constraints on certain subsets

1991 ◽  
Vol 43 (3) ◽  
pp. 451-462 ◽  
Author(s):  
Hiroaki Komatsu ◽  
Hisao Tominaga
Keyword(s):  
Commutativity Theorems ◽  
Unital Rings ◽  
Polynomial Constraints

We prove several commutativity theorems for unital rings with polynomial constraints on certain subsets, which improve and generalise the recent results of Grosen, and Ashraf and Quadri.

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