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.

Factors Involved in the Production of Annual Zones on the Scales of the Rainbow Trout (Salmo Irideus). II

1932 ◽  
Vol 9 (1) ◽  
pp. 6-11
Author(s):  
D. BHATIA
Keyword(s):  
Rainbow Trout ◽  
Direct Effect ◽  
Low Temperatures ◽  
Fish Scales ◽  
Periodic Rings ◽  
High And Low Temperatures

1. Rainbow trout fed uniformly does not exhibit any periodic zones on its scales whether the temperature is normal or high or low. 2. At both high and low temperatures (17° C. and 4° C.) fish fed abundantly show on their scales a peripheral band of comparatively broad rings, and fish starved show a peripheral band of narrow rings. 3. Bands of broad and narrow rings, resembling the so-called "annual zones," could be produced on the scales by altering the food supplies of the fish irrespective of the temperature of the medium. 4. Variations in temperature have no direct effect on the production of the periodic rings on the fish scales.

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