Characterizing Jordan n-Derivations of Unital Rings Containing Idempotents

2020 ◽  
Vol 46 (6) ◽  
pp. 1639-1658
Author(s):  
Xiaofei Qi ◽  
Zhiling Guo ◽  
Ting Zhang
Keyword(s):  
Unital Rings

Invo-fine unital rings

2016 ◽  
Vol 11 ◽  
pp. 841-843 ◽  
Author(s):  
Peter V. Danchev
Keyword(s):  
Unital Rings

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-sideds-unital rings

1992 ◽  
Vol 15 (4) ◽  
pp. 813-818
Author(s):  
H. A. S. Abujabal ◽  
M. A. Khan
Keyword(s):  
Polynomial Identity ◽  
Unital Ring ◽  
Unital Rings

The following theorem is proved: Letr=r(y)>1,s, andtbe non-negative integers. IfRis a lefts-unital ring satisfies the polynomial identity[xy−xsyrxt,x]=0for everyx,y∈R, thenRis commutative. The commutativity of a rights-unital ring satisfying the polynomial identity[xy−yrxt,x]=0for allx,y∈R, is also proved.

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 INVO-CLEAN UNITAL RINGS

2017 ◽  
Vol 32 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Peter V. Danchev
Keyword(s):  
Unital Rings

scholarly journals Rings in which every element is either a sum or a difference of a nilpotent and an idempotent

2016 ◽  
Vol 15 (08) ◽  
pp. 1650148 ◽  
Author(s):  
Simion Breaz ◽  
Peter Danchev ◽  
Yiqiang Zhou
Keyword(s):  
Division Ring ◽  
Matrix Ring ◽  
Decomposition Theorem ◽  
Arbitrary Ring ◽  
Clean Rings ◽  
Clean Ring ◽  
Unital Rings ◽  
Nil Clean Ring ◽  
Comprehensive Study

Generalizing the notion of nil-cleanness from [A. J. Diesl, Nil clean rings, J. Algebra 383 (2013) 197–211], in parallel to [P. V. Danchev and W. Wm. McGovern, Commutative weakly nil clean unital rings, J. Algebra 425 (2015) 410–422], we define the concept of weak nil-cleanness for an arbitrary ring. Its comprehensive study in different ways is provided as well. A decomposition theorem of a weakly nil-clean ring is obtained. It is completely characterized when an abelian ring is weakly nil-clean. It is also completely determined when a matrix ring over a division ring is weakly nil-clean.

scholarly journals Commutative weakly nil clean unital rings

2015 ◽  
Vol 425 ◽  
pp. 410-422 ◽  
Author(s):  
Peter V. Danchev ◽  
W.Wm. McGovern
Keyword(s):  
Unital Rings

Unital rings whose additive endomorphisms commute

1977 ◽  
Vol 228 (3) ◽  
pp. 197-214 ◽  
Author(s):  
R. A. Bowshell ◽  
P. Schultz
Keyword(s):  
Unital Rings

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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