The Rings Which Can Be Recovered by Means of the Difference

Ivan Chajda; Filip Švrček

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

The rings which are Boolean. II.

P. Jedlička (2012)

Acta Universitatis Carolinae. Mathematica et Physica

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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 rings satisfying certain polynomial identities.

Maurer, I.Gy., Szigeti, J. (1990)

Mathematica Pannonica

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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 $m \geq 0, r \geq 0, s \geq 0, q \geq 0$ be fixed integers. Suppose that $R$ is an associative ring with unity $1$ in which for each $x, y \in R$ there exist polynomials $f (X) \in X^{2} Z Z [X], g (X), h (X) \in X Z Z [X]$ 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.

Rings with divisibility on descending chains of ideals

Oussama Aymane Es Safi, Najib Mahdou, Ünsal Tekir (2024)

Czechoslovak Mathematical Journal

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This paper deals with the rings which satisfy $D C C_{d}$ condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings...