periodic ring
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2019 ◽  
Vol 19 (12) ◽  
pp. 2050235 ◽  
Author(s):  
Jian Cui ◽  
Peter Danchev

A ring [Formula: see text] is called periodic if, for every [Formula: see text] in [Formula: see text], there exist two distinct positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text]. The paper is devoted to a comprehensive study of the periodicity of arbitrary unital rings. Some new characterizations of periodic rings and their relationship with strongly [Formula: see text]-regular rings are provided as well as, furthermore, an application of the obtained main results to a ∗-version of a periodic ring is being considered. Our theorems somewhat considerably improved on classical results in this direction.


2018 ◽  
Vol 6 (6) ◽  
pp. 579 ◽  
Author(s):  
Yan Zhi ◽  
Xiangbo Yang ◽  
Jiaye Wu ◽  
Shiping Du ◽  
Peichao Cao ◽  
...  

Author(s):  
Zhao Chen ◽  
Qi Zhang ◽  
Fan Zhang ◽  
Ying Gu ◽  
Qihuang Gong
Keyword(s):  

2011 ◽  
Vol 41 (5) ◽  
pp. 441-446 ◽  
Author(s):  
A A Antipov ◽  
S M Arakelyan ◽  
Vladimir I Emel'yanov ◽  
S P Zimin ◽  
S V Kutrovskaya ◽  
...  

2008 ◽  
Vol 15 (02) ◽  
pp. 199-206
Author(s):  
H. R. Dorbidi

Let S be a semigroup. The degree of S is the smallest natural number r such that for each x ∈ S, xn(x)+r = xn(x), where n(x) ∈ ℕ. If such a number r does not exist, we say that the degree of S is infinite. For a group G, this coincides with the exponent of G. We prove that for a periodic ring R, the degree of R equals exp (U(R)), where U(R) denotes the unit group of R. Then we determine all degrees for any rings.


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