Results 31 to 40 of about 702,392 (300)

ON SEMIDERIVATIONS OF PRIME RINGS

Demonstratio Mathematica, 2004
Summary: A semiderivation of a ring \(R\) is an additive mapping \(f\colon R\to R\) together with a function \(g\colon R\to R\) such that \(f(xy)=f(x)g(y)+xf(y)=f(x)y+g(x)f(y)\) and \(f(g(x))=g(f(x))\) for all \(x,y\in R\). If \(f\) is a non-zero semiderivation of a prime ring \(R\), then it is known that \(g\) must necessarily be an endomorphism. Let \
Ashraf, Mohammad, Nadeem-ur-Rehman
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A Generalization of the Prime Radical of Rings

Natural and Applied Sciences Journal, 2023
Let $R$ be a ring, $I$ be an ideal of $R$, and $\sqrt{I}$ be a prime radical of $I$. This study generalizes the prime radical of $\sqrt{I}$ where it denotes by $\sqrt[n+1]{I}$, for $n\in \mathbb{Z}^{+}$. This generalization is called $n$-prime radical of ideal $I$.
Didem KARALARLIOĞLU CAMCI, Didem YEŞİL, Rasie MEKERA, Çetin CAMCI   +3 more
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Primes in products of rings [PDF]

Pacific Journal of Mathematics, 1971
This paper is an elementary note which indicates how Harrison's primes sit in certain kinds of rings. It is proved that primes behave nicely under finite direct products. Also it is shown that any nil ideal is a subset of every prime. This gives information about the primes of artinian rings.
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DERIVATIONS ON PRIME AND SEMI-PRIME RINGS

Bulletin of the Korean Mathematical Society, 2002
Several results concerning derivations on rings and Banach algebras are proved. A sample theorem: Let \(n\) be a positive integer and let \(R\) be an \(n!\)-torsionfree semiprime ring. If \(D\) and \(G\) are derivations on \(R\) such that \([D^2(x)+G(x),x^n]=0\) for all \(x\in R\), then \([D(x),x]=[G(x),x]=0\) for all \(x\in R\).
Lee, Eun Hwi, Jung, Yong-Soo, Chang, Ick-Soon   +2 more
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Characteristic of Rings. Prime Fields

Formalized Mathematics, 2015
Summary The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over
Christoph Schwarzweller, Artur Kornilowicz   +1 more
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About unital and non-unital duo rings [PDF]

Proceedings of the Estonian Academy of Sciences
Several results about one-sided duo rings and duo rings are generalized from the case of unital rings to the case of arbitrary associative rings in this paper.
Mart Abel, Eva-Lotta Elmanovitš
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On rings with prime centers

International Journal of Mathematics and Mathematical Sciences, 1994
Let R be a ring, and let C denote the center of R. R is said to have a prime center if whenever ab belongs to C then a belongs to C or b belongs to C. The structure of certain classes of these rings is studied, along with the relation of the notion of ...
Hazar Abu-Khuzam, Adil Yaqub
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SOME IDENTITIES INVOLVING ENDOMORPHISMS OF PRIME RINGS [PDF]

Journal of Algebraic Systems
In this paper we will extend some results on the commutativity of quotient rings proved in [1] and [11]. However, we will consider endomorphisms instead of derivations and generalized derivations, which is sufficient to obtain good results.
Abdelkarim Boua
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Dependent Automorphisms in Prime Rings [PDF]

Canadian Mathematical Bulletin, 1998
AbstractFor each n ≥ 4 we construct a class of examples of a minimal C dependent set of n automorphisms of a prime ring R, where C is the extended centroid of R. For n = 4 and n = 5 it is shown that the preceding examples are completely general, whereas for n = 6 an example is given which fails to enjoy any of the nice properties of the above example.
Brešar, Matej, Martindale, W. S., Miers, C. Robert   +2 more
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On (?,?)-Derivations and Commutativity of Prime and Semi prime ?-rings

مجلة بغداد للعلوم, 2016
Let R be a ?-ring, and ?, ? be two automorphisms of R. An additive mapping d from a ?-ring R into itself is called a (?,?)-derivation on R if d(a?b) = d(a)? ?(b) + ?(a)?d(b), holds for all a,b ?R and ???. d is called strong commutativity preserving (SCP)
Baghdad Science Journal
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