scholarly journals SOME RESULTS OF GENERALIZED LEFT (θ,θ)-DERIVATIONS ON SEMIPRIME RINGS

2015 ◽  
Vol 11 (8) ◽  
pp. 5529-5535
Author(s):  
Ikram A. Saed
Keyword(s):  
Associative Ring ◽  
Semiprime Rings ◽  
Definition Of

Let R be an associative ring with center Z(R) . In this paper , we study the commutativity of semiprime rings under certain conditions , it comes through introduce the definition of generalized left(θ,θ)- derivation associated with left (θ,θ) -derivation , where Î¸ is a mapping on R .

scholarly journals Generalized Derivations and Left Ideals in Prime and Semiprime Rings

ISRN Algebra ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-5 ◽  
Author(s):  
Basudeb Dhara ◽  
Atanu Pattanayak
Keyword(s):  
Left Ideal ◽  
Associative Ring ◽  
Generalized Derivation ◽  
Generalized Derivations ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings

Let R be an associative ring, λ a nonzero left ideal of R, d:R→R a derivation and G:R→R a generalized derivation. In this paper, we study the following situations in prime and semiprime rings: (1) G(x∘y)=a(xy±yx); (2) G[x,y]=a(xy±yx); (3) d(x)∘d(y)=a(xy±yx); for all x,y∈λ and a∈{0,1,-1}.

scholarly journals Generalized (; )-derivations and Left Ideals in Prime and Semiprime Rings

2017 ◽  
Vol 13 (2) ◽  
pp. 7163-7167
Author(s):  
Asma Ali ◽  
Hamidur Rahaman
Keyword(s):  
Left Ideal ◽  
Associative Ring ◽  
Generalized Derivation ◽  
Generalized Derivations ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings

Let R be an associative ring, ; be the automorphisms of R, be a nonzero left ideal of R, F : R ! R be a generalized (; )-derivation and d : R ! Rbe an (; )-derivation. In the present paper we discuss the following situations: (i) F(xoy) = a(xy yx), (ii) F([x; y]) = a(xy yx), (iii) d(x)od(y) = a(xy yx) forall x; y 2 and a 2 f0; 1;ô€€€1g. Also some related results have been obtained.

A study of derivable mappings of semiprime rings

2018 ◽  
Vol 7 (1-2) ◽  
pp. 19-26
Author(s):  
Gurninder S. Sandhu ◽  
Deepak Kumara
Keyword(s):  
Associative Ring ◽  
Semiprime Ring ◽  
Nonzero Ideal ◽  
Lie Ideal ◽  
Commutativity Theorems ◽  
Semiprime Rings

Throughout this note, \(R\) denotes an associative ring and \(C(R)\) be the center of \(R\). In this paper, it isproved that a non-central Lie ideal \(L\) of a semiprime ring \(R\) contains a nonzero ideal of \(R\) and this result isused to obtain several commutativity theorems of \(R\) involving multiplicative derivations. Moreover, someresults on one-sided ideals of \(R\) are given.

scholarly journals The Generalized Inverse A(2)T, Sof a Matrix Over an Associative Ring

2007 ◽  
Vol 83 (3) ◽  
pp. 423-438 ◽  
Author(s):  
Yaoming Yu ◽  
Guorong Wang
Keyword(s):  
Associative Ring ◽  
Generalized Inverse ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Drazin Inverse ◽  
Group Inverse ◽  
Arbitrary Matrix ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Explicit Expressions

AbstractIn this paper we establish the definition of the generalized inverse A(2)T, Swhich is a {2} inverse of a matrixAwith prescribed imageTand kernelsover an associative ring, and give necessary and sufficient conditions for the existence of the generalized inverseand some explicit expressions forof a matrix A over an associative ring, which reduce to the group inverse or {1} inverses. In addition, we show that for an arbitrary matrixAover an associative ring, the Drazin inverse Ad, the group inverse Agand the Moore-Penrose inverse. if they exist, are all the generalized inverse A(2)T, S.

Extending Jordan Ideals and Jordan Homomorphisms of Symmetric Elements in a Ring with Involution

1972 ◽  
Vol 24 (1) ◽  
pp. 50-59 ◽  
Author(s):  
Kirby C. Smith
Keyword(s):  
Associative Ring ◽  
Background Information ◽  
Matrix Rings ◽  
Jordan Ring ◽  
Jordan Homomorphism ◽  
Rings With Involution ◽  
Jordan Homomorphisms ◽  
Definition Of ◽  
Natural Way

In this work, we show how the ideas in [3, pp. 6-12] can be used to give conditions under which Jordan ideals in the set of symmetric elements in an associative ring R with involution extend to associative ideals of R in a natural way. We also give conditions under which a Jordan homomorphism of the set of symmetric elements will extend to an associative homomorphism of R. Such work has been done on matrix rings with involution in [5; 6]. An abstract definition of a Jordan ring may be found in [3] as well as other background information.

scholarly journals On dependent elements in rings

2004 ◽  
Vol 2004 (54) ◽  
pp. 2895-2906 ◽  
Author(s):  
Joso Vukman ◽  
Irena Kosi-Ulbl
Keyword(s):  
Associative Ring ◽  
Semiprime Ring ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Alpha Beta

LetRbe an associative ring. An elementa∈Ris said to be dependent on a mappingF:R→Rin caseF(x)a=axholds for allx∈R. In this paper, elements dependent on certain mappings on prime and semiprime rings are investigated. We prove, for example, that in case we have a semiprime ringR, there are no nonzero elements which are dependent on the mappingα+β, whereαandβare automorphisms ofR.

scholarly journals ON JORDAN IDEAL IN PRIME AND SEMIPRIME INVERSE SEMIRINGS WITH CENTRALIZER

2020 ◽  
Vol 30 (4) ◽  
pp. 77
Author(s):  
Rawnaq Khaleel Ibraheem ◽  
Abdulrahman H. Majeed
Keyword(s):  
Lie Ideal ◽  
Semiprime Rings ◽  
Definition Of

     In this paper we recall the definition of centralizer on inverse semiring. Also introduce the definition of Jordan ideal and Lie ideal. Some results of M.A.Joso Vukman on centralizers on semiprime rings are generalized here to inverse semirings.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

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