Results 151 to 160 of about 2,459,145 (179)

On Derivations of Centralizer Near-Rings

Taiwanese Journal of Mathematics, 2011
It is proved that if a centralizer near-ring N has a nonzero derivation, then N is a near-field.
Y Fong
exaly   +3 more sources

Characterization and Commuting Probability of n-Centralizer Finite Rings

Proyecciones, 2023
Let R be a finite ring. The commuting probability of R is the probability that any two randomly chosen elements of R commute. A ring R is called an n-centralizer ring if it has n distinct centralizers.
Rajat Kanti Nath, Dhiren Kumar Basnet
exaly   +2 more sources

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Matrix Near-Rings Over Centralizer Near-Rings

Algebra Colloquium, 2000
In the most widely accepted definition of matrix near-rings [\textit{J. D. P. Meldrum} and \textit{A. P. J. van der Walt}, Arch. Math. 47, 312-319 (1986; Zbl 0611.16025)], there are two obvious ways of linking ideals in the base near-ring to ideals in the matrix near-ring.
Leon van Wyk, Kirby C Smith
exaly   +2 more sources

When Is a Centralizer Near-Ring Isomorphic to a Matrix Near-Ring?

Communications in Algebra, 1996
Leon van Wyk, Kirby C Smith
exaly   +2 more sources

Centralizer Near-Rings, Matrix Near-Rings and Cyclic p-Groups

Algebra Colloquium, 2005
If G is a finite group and [Formula: see text] is a group of automorphisms of G, then it is known that the matrix near-ring [Formula: see text] is a subnear-ring of the centralizer near-ring [Formula: see text] for every m ≥ 2. Conditions are known under which [Formula: see text] is a proper subnear-ring of [Formula: see text], and if [Formula: see ...
Leon van Wyk, Kirby C. Smith
exaly   +3 more sources

The Lattice of Left Ideals in a Centralizer Near-Ring Is Distributive [PDF]

Proceedings of the American Mathematical Society, 1982
A decomposition theorem for a left ideal in a finite centralizer near-ring is established. This result is used to show that the lattice of left ideals in a finite centralizer near-ring is distributive.
Kirby C. Smith
exaly   +3 more sources

The Group of Units of Centralizer Near-Rings

Communications in Algebra, 1984
C J Maxson
exaly   +2 more sources

On Semisimple Rings That Are Centralizer Near-Rings [PDF]

Pacific Journal of Mathematics, 1982
Maxson, Carlton J., Pettet, Martin R., Smith, Kirby C.   +2 more
exaly   +4 more sources

Endomorphism Rings Are Centralizer Near-Rings

GANIT Journal of Bangladesh Mathematical Society, 2016
For a finite ring R with identity and a finite unital R-module V the set C(R; V) = {f : V ->V : f(?v) = ?f(v) for all ? ? R, v ? V} is the centralizer near-ring determined by R and V. Rings R for witch C(R; V) is a ring for every R-module V, are characterized. Conditions are given under which C(R; V) is a semisimple centralizer near ring.
Satrajit Kumar Saha, Md Rezaul Islam
exaly   +3 more sources

Centralizer Near-Rings Determined by PID-Modules, II

Periodica Mathematica Hungarica, 1993
[For part I cf. Arch. Math. 56, No. 2, 140-147 (1991; Zbl 0706.16026).] The authors answer an open problem in radical theory by giving an example of a zero-symmetric simple near-ring with identity such that \(J_ 2(N) = N\). This is in contrast to the situation for rings, since every simple ring with identity is semisimple in the sense of Jacobson.
C J Maxson
exaly   +2 more sources