Displaying similar documents to “The Rings Which Can Be Recovered by Means of the Difference”

Restricted Boolean group rings

Dinesh Udar, R.K. Sharma, J.B. Srivastava (2017)

Archivum Mathematicum

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In this paper we study restricted Boolean rings and group rings. A ring R is 𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑𝐵𝑜𝑜𝑙𝑒𝑎𝑛 if every proper homomorphic image of R is boolean. Our main aim is to characterize restricted Boolean group rings. A complete characterization of non-prime restricted Boolean group rings has been obtained. Also in case of prime group rings necessary conditions have been obtained for a group ring to be restricted Boolean. A counterexample is given to show that these conditions are not sufficient.

On a theorem of McCoy

Rajendra K. Sharma, Amit B. Singh (2024)

Mathematica Bohemica

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We study McCoy’s theorem to the skew Hurwitz series ring ( HR , ω ) for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring R satisfies McCoy’s theorem of skew Hurwitz series.

Commutativity of associative rings through a Streb's classification

Mohammad Ashraf (1997)

Archivum Mathematicum

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Let m ≥ 0 , r ≥ 0 , s ≥ 0 , q ≥ 0 be fixed integers. Suppose that R is an associative ring with unity 1 in which for each x , y ∈ R there exist polynomials f ( X ) ∈ X 2 Z Z [ X ] , g ( X ) , h ( X ) ∈ X Z Z [ X ] such that { 1 - g ( y x m ) } [ x , x r y - x s f ( y x m ) x q ] { 1 - h ( y x m ) } = 0 . Then R is commutative. Further, result is extended to the case when the integral exponents in the above property depend on the choice of x and y . Finally, commutativity of one sided s-unital ring is also obtained when R satisfies some related ring properties.