COMMUTATIVITY OF π-STRONGLY PERIODIC RINGS

2020 ◽  
pp. 121-134
Author(s):  
Saeed Nasirifar ◽  
Shaban Ali Safari Sabet
Keyword(s):  
Periodic Rings

scholarly journals A note on a theorem of Jacobson related to periodic rings

2020 ◽  
Vol 148 (12) ◽  
pp. 5087-5089
Author(s):  
D. D. Anderson ◽  
P. V. Danchev
Keyword(s):  
Periodic Rings

Some Commutativity Results For Periodic Rings

2017 ◽  
Vol 43 (2) ◽  
pp. 93-97
Author(s):  
Y.Madana Mohana Reddy ◽  
◽  
G.Shobha latha ◽  
D.V.Rami Reddy
Keyword(s):  
Periodic Rings

Weakly periodic rings with conditions on commutators

1996 ◽  
Vol 71 (1-2) ◽  
pp. 145-153
Author(s):  
H. Abu-Khuzam ◽  
M. Hasanali ◽  
A. Yaqub
Keyword(s):  
Periodic Rings

scholarly journals Commutative subrings of periodic rings.

1976 ◽  
Vol 39 ◽  
pp. 161 ◽  
Author(s):  
Thomas J. Laffey
Keyword(s):  
Periodic Rings

Some new characterizations of periodic rings

2019 ◽  
Vol 19 (12) ◽  
pp. 2050235 ◽  
Author(s):  
Jian Cui ◽  
Peter Danchev
Keyword(s):  
Periodic Ring ◽  
Periodic Rings ◽  
Positive Integers ◽  
Unital Rings ◽  
Regular Rings ◽  
Comprehensive Study

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.

scholarly journals Periodic rings with commuting nilpotents

1984 ◽  
Vol 7 (2) ◽  
pp. 403-406
Author(s):  
Hazar Abu-Khuzam ◽  
Adil Yaqub
Keyword(s):  
Positive Integer ◽  
Commutative Ring ◽  
Finite Fields ◽  
Boolean Ring ◽  
Fixed Integer ◽  
Integer Coefficients ◽  
Nilpotent Elements ◽  
Periodic Rings

LetRbe a ring (not necessarily with identity) and letNdenote the set of nilpotent elements ofR. Suppose that (i)Nis commutative, (ii) for everyxinR, there exists a positive integerk=k(x)and a polynomialf(λ)=fx(λ)with integer coefficients such thatxk=xk+1f(x), (iii) the setIn={x|xn=x}wherenis a fixed integer,n>1, is an ideal inR. ThenRis a subdirect sum of finite fields of at mostnelements and a nil commutative ring. This theorem, generalizes the “xn=x” theorem of Jacobson, and (takingn=2) also yields the well known structure of a Boolean ring. An Example is given which shows that this theorem need not be true if we merely assume thatInis a subring ofR.

scholarly journals On structure of certain periodic rings and near-rings

2000 ◽  
Vol 24 (10) ◽  
pp. 667-672
Author(s):  
Moharram A. Khan
Keyword(s):  
Decomposition Theorem ◽  
Periodic Rings

The aim of this work is to study a decomposition theorem for rings satisfying either of the propertiesxy=xpf(xyx)xqorxy=xpf(yxy)xq, wherep=p(x,y),q=q(x,y)are nonnegative integers andf(t)∈tℤ[t]vary with the pair of elementsx,y, and further investigate the commutativity of such rings. Other related results are obtained for near-rings.

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