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1

Green’s relations in the commutative centralizers of monounary algebras

Jakubíková-Studenovská D., Šuličová M.

Demonstratio Mathematica

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2015

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Vol. 48, nr 4

536--545

EN

The paper deals with the monounary algebras for which the second centralizer equals the first centralizer. We describe Green’s relations on the semigroup C, where C is the centralizer of such algebra.

2

On Jordan triple α-* centralizers of semiprime rings

Ashraf M., Mozumder M.R., Khan A.

Demonstratio Mathematica

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2014

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Vol. 47, nr 1

130--136

EN

Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R → R is called a left (resp. right) Jordan α-* centralizer associated with a function α : R → R if T(x2) = T(x)α(x*) (resp. T(x2) = α(x*)T(x)) holds for all x (…) R. If T is both left and right Jordan α-* centralizer of R, then it is called Jordan α-* centralizer of R. In the present paper it is shown that if α is an automorphism of R, and T : R → R is an additive mapping such that 2T(xyx) = T(x)α(y*x*) + α(x*y*)T(x) holds for all x; y (…) R, then T is a Jordan α-* centralizer of R.

3

On (…)-centralizers of semiprime rings

Huang S., Haetinger C.

Demonstratio Mathematica

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2012

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Vol. 45, nr 1

29-34

EN

Let R be a semiprime ring with center Z(R) and (…) be a surjective ho-omorphism. In this paper, we prove that T is a (…)-centralizer if one of the following holds: (…).

4

Jordan structure on prime rings with centralizers

Majeed A., Asmaiel H.

Demonstratio Mathematica

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2007

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Vol. 40, nr 3

529-536

EN

Our object in this paper is to study the generalization of Borut Zalar result in [1] on Jordan centralizer of semiprime rings by prove the following result: Let R be a prime of characteristic different from 2, and U be a Jordan ideal of R. If T is an additive mapping from R to itself satisfying the following condition T(ur + ru) = uT(r) + T(r)u, then T(ur) = uT(r), for all r is an element of R, u is an element of U.

5

A note centralizers in semiprime rings

Kosi-Ulbl I.

Demonstratio Mathematica

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2005

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Vol. 38, nr 2

277--282

EN

The purpose of this paper is to prove the following result: Let R be a (m+n + 2)! and 3m2n + 3mn2 + 4m2 + 4n2 +10mn-torsion free semiprime ring with an identity element and let T : R -R be an additive mapping such that 3T(xm+n+1) = T(x)xm+n + xmT(x)xn + xm=nT(x) is fulfilled for all x is an element R and some fixed nonnegative integers m and n, m+n=0. In this case T is a centralizer.

6

On normalizers and centralizers of compact Lie groups. Applications to structural probability theory

Hazod W.

Probability and Mathematical Statistics

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2003

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Vol. 23, Fasc. 1

39--60

EN

The concept of operator stability on finite-dimensional vector spaces V was generalized in the past into several directions. In particular, operator-semistable and self-decomposable laws and self-similar processes were investigated and the underlying vector space V may be replaced by a simply connected nilpotent Lie group G. This motivates investigations of certain linear subgroups of GL (V) and Aut (G), respectively, the decomposability group of a full probability μ and its compact normal subgroup, the invariance group. Using some basic properties of algebraic groups, the structure of normalizers and centralizers of compact matrix groups is analyzed and applied to the above-mentioned set-up, proving the existence and describing the shape of exponents and of commuting exponents of (operator-) semistable laws. Further applications are mentioned, in particular for operator self-decomposable laws and self-similar processes.