Abstract and Applied Analysis, ISSN 1085-3375, 7/2013, Volume 2013, pp. 1 - 5

We study the stability and hyperstability of cubic Lie derivations on normed algebras. At the end, we write some additional observations about our results.

MATHEMATICS, APPLIED | ULAM-RASSIAS STABILITY | Mathematical research | Approximation theory | Research | Studies | Probability | Writing | Algorithms | Algebra | Physics | Derivation | Stability | Approximation

MATHEMATICS, APPLIED | ULAM-RASSIAS STABILITY | Mathematical research | Approximation theory | Research | Studies | Probability | Writing | Algorithms | Algebra | Physics | Derivation | Stability | Approximation

Journal Article

The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2011, Volume 41, Issue 3, pp. 765 - 776

The purpose of this paper is to prove the following result. Let m and n be positive integers, and let R be a prime ring with char (R) = 0 or m + n + 1 ≤ char...

Integers | Mathematical rings | Polynomials | Mathematical theorems | Algebra | Linearization | Functional identity | Prime ring | Two-sided centralizer | MATHEMATICS | two-sided centralizer | functional identity | 39B05 | 16N60

Integers | Mathematical rings | Polynomials | Mathematical theorems | Algebra | Linearization | Functional identity | Prime ring | Two-sided centralizer | MATHEMATICS | two-sided centralizer | functional identity | 39B05 | 16N60

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 12/2015, Volume 65, Issue 6, pp. 1271 - 1276

In this paper we prove the following result. Let R be a 2-torsion free semiprime ring and let f : R → R be an additive mapping satisfying the relation f(x)x +...

centralizing mapping | commuting mapping | skew-commuting mapping | additive mapping | derivation | semiprime ring | prime ring | BANACH-ALGEBRAS | DERIVATIONS | PRIME-RINGS | MATHEMATICS | MAPS | CENTRALIZING MAPPINGS | Rings (Algebra) | Research | Mathematical research | Mappings (Mathematics)

centralizing mapping | commuting mapping | skew-commuting mapping | additive mapping | derivation | semiprime ring | prime ring | BANACH-ALGEBRAS | DERIVATIONS | PRIME-RINGS | MATHEMATICS | MAPS | CENTRALIZING MAPPINGS | Rings (Algebra) | Research | Mathematical research | Mappings (Mathematics)

Journal Article

Proceedings - Mathematical Sciences, ISSN 0253-4142, 11/2014, Volume 124, Issue 4, pp. 497 - 500

The main purpose of this paper is to prove the following result: Let n > 1 be a fixed integer, let R be a n!-torsion free semiprime ring, and let f : R → R...

Prime ring | 16N60, 16R50 | centralizing mapping | commuting mapping | additive mapping | Mathematics, general | Mathematics | derivation | semiprime ring | functional identity | Functional identity | Commuting mapping | Semiprime ring | Derivation | Centralizing mapping | Additive mapping | MATHEMATICS | CENTRALIZING MAPPINGS | DERIVATIONS | PRIME-RINGS | Rings (Algebra) | Research | Mathematical research | Mappings (Mathematics)

Prime ring | 16N60, 16R50 | centralizing mapping | commuting mapping | additive mapping | Mathematics, general | Mathematics | derivation | semiprime ring | functional identity | Functional identity | Commuting mapping | Semiprime ring | Derivation | Centralizing mapping | Additive mapping | MATHEMATICS | CENTRALIZING MAPPINGS | DERIVATIONS | PRIME-RINGS | Rings (Algebra) | Research | Mathematical research | Mappings (Mathematics)

Journal Article

Arabian Journal of Mathematics, ISSN 2193-5343, 9/2018, Volume 7, Issue 3, pp. 189 - 193

Let R be a prime ring with the extended centroid C and symmetric Martindale quotient ring $$Q_s(R)$$ Qs(R) . In this paper we prove the following result. Let...

Mathematics, general | 16W25 | Mathematics | 16N60 | Derivation

Mathematics, general | 16W25 | Mathematics | 16N60 | Derivation

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 11/2019, Volume 42, Issue 6, pp. 3131 - 3147

In this paper, we prove the following result. Let $$m\ge 1,n\ge 1$$ m ≥ 1 , n ≥ 1 be some fixed integers and let R be a prime ring with $$\mathrm{char}(R)=0$$...

Semiprime ring | Two-sided centralizer | 39B05 | Mathematics | Left (right) Jordan centralizer | Prime ring | Functional identity | Left (right) centralizer | Ring | ( m , n )-Jordan centralizer | Mathematics, general | Applications of Mathematics | 16W10 | MATHEMATICS | Left (right) centralizer | Left (right) Jordan centralizer | (m, n)-Jordan centralizer | Integers | Functional equations | Oil field equipment

Semiprime ring | Two-sided centralizer | 39B05 | Mathematics | Left (right) Jordan centralizer | Prime ring | Functional identity | Left (right) centralizer | Ring | ( m , n )-Jordan centralizer | Mathematics, general | Applications of Mathematics | 16W10 | MATHEMATICS | Left (right) centralizer | Left (right) Jordan centralizer | (m, n)-Jordan centralizer | Integers | Functional equations | Oil field equipment

Journal Article

7.
Full Text
On Functional Equation Related to a Class of Generalized Inner Derivations in Prime Rings

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 4/2018, Volume 41, Issue 2, pp. 687 - 707

The main purpose of this paper is to prove the following result. Let R be a prime ring of $$\mathrm{char}(R)=0$$ char(R)=0 or $$\mathrm{char}(R)>4,$$...

Semiprime ring | Jordan triple derivation | Functional equation | Derivation | 39B05 | Mathematics | Ring with involution | Prime ring | Functional identity | Ring | Mathematics, general | Applications of Mathematics | Generalized inner derivation | Inner derivation | Jordan derivation | 16W10 | SPACES | STANDARD OPERATOR-ALGEBRAS | MATHEMATICS | SEMIPRIME RINGS | BICIRCULAR PROJECTIONS | JORDAN DERIVATIONS | BI-CIRCULAR PROJECTIONS | Functional equations | Quotients

Semiprime ring | Jordan triple derivation | Functional equation | Derivation | 39B05 | Mathematics | Ring with involution | Prime ring | Functional identity | Ring | Mathematics, general | Applications of Mathematics | Generalized inner derivation | Inner derivation | Jordan derivation | 16W10 | SPACES | STANDARD OPERATOR-ALGEBRAS | MATHEMATICS | SEMIPRIME RINGS | BICIRCULAR PROJECTIONS | JORDAN DERIVATIONS | BI-CIRCULAR PROJECTIONS | Functional equations | Quotients

Journal Article

IOP Conference Series: Materials Science and Engineering, ISSN 1757-8981, 11/2018, Volume 450, Issue 2

Conference Proceeding

Aequationes mathematicae, ISSN 0001-9054, 6/2013, Volume 85, Issue 3, pp. 329 - 346

Let m ≥ 0, n ≥ 0 be fixed integers with m + n ≠ 0 and let R be a prime ring with char(R) = 0 or m + n + 1 ≤ char(R) ≠ 2. Suppose that there exists an additive...

Prime ring | Analysis | right centralizer | Mathematics | two-sided centralizer | Combinatorics | semiprime ring | left centralizer | 16N60 | MATHEMATICS | MATHEMATICS, APPLIED | Algebra | Integers | Oil field equipment | Additives | Mapping | Mathematical analysis

Prime ring | Analysis | right centralizer | Mathematics | two-sided centralizer | Combinatorics | semiprime ring | left centralizer | 16N60 | MATHEMATICS | MATHEMATICS, APPLIED | Algebra | Integers | Oil field equipment | Additives | Mapping | Mathematical analysis

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 7/2016, Volume 39, Issue 3, pp. 885 - 899

The purpose of this paper is to prove the following result. Let R be a prime ring of characteristic different from two and let $$D:R\rightarrow R$$ D : R → R...

Prime ring | Functional identity | Semiprime ring | Jordan triple derivation | Derivation | 39B05 | Mathematics, general | Mathematics | Applications of Mathematics | Jordan derivation | 16W10 | MATHEMATICS | SEMIPRIME RINGS | MAPPINGS | JORDAN DERIVATIONS

Prime ring | Functional identity | Semiprime ring | Jordan triple derivation | Derivation | 39B05 | Mathematics, general | Mathematics | Applications of Mathematics | Jordan derivation | 16W10 | MATHEMATICS | SEMIPRIME RINGS | MAPPINGS | JORDAN DERIVATIONS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2007, Volume 420, Issue 2, pp. 596 - 608

It is shown that for many finite dimensional normed vector spaces V over C , a linear projection P : V → V will have nice structure if P + λ( I − P) is an...

Unitary similarity invariant norms | Unitary congruence invariant norms | Bicircular projection | Unitarily invariant norms | Symmetric norms | symmetric norms | unitary similarity invariant norms | MATRIX | MATHEMATICS, APPLIED | unitarily invariant norms | unitary congruence invariant norms | bicircular projections | ISOMETRIES | Universities and colleges

Unitary similarity invariant norms | Unitary congruence invariant norms | Bicircular projection | Unitarily invariant norms | Symmetric norms | symmetric norms | unitary similarity invariant norms | MATRIX | MATHEMATICS, APPLIED | unitarily invariant norms | unitary congruence invariant norms | bicircular projections | ISOMETRIES | Universities and colleges

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 08/2016, Volume 66, Issue 4, pp. 811 - 814

In this paper we prove the following result. Let be a !-torsion free semiprime ring and let : → be an additive mapping satisfying the relation + ) = 0 for all...

16R50 | centralizing mapping | commuting mapping | skew-commuting mapping | Primary 16N60 | additive mapping | derivation | functional identities | semiprime ring | prime ring | IDENTITIES | BANACH-ALGEBRAS | DERIVATIONS | ADDITIVE MAPPINGS | PRIME-RINGS | MATHEMATICS | CENTRALIZING MAPPINGS | Rings (Algebra) | Research | Mathematical research | Mappings (Mathematics)

16R50 | centralizing mapping | commuting mapping | skew-commuting mapping | Primary 16N60 | additive mapping | derivation | functional identities | semiprime ring | prime ring | IDENTITIES | BANACH-ALGEBRAS | DERIVATIONS | ADDITIVE MAPPINGS | PRIME-RINGS | MATHEMATICS | CENTRALIZING MAPPINGS | Rings (Algebra) | Research | Mathematical research | Mappings (Mathematics)

Journal Article

The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2012, Volume 42, Issue 4, pp. 1153 - 1168

The purpose of this paper is to prove the following result. Let m, n ≥ 1 be some fixed integers with m ≠ n, and let R be a prime ring with (m + n)² < char (R)....

Integers | Commutativity | Mathematical theorems | Algebra | Logical proofs | Mathematical rings | Polynomials | Commuting | Linearization | Prime ring | (m, n)-Jordan derivation | Semiprime ring | Derivation | Left derivation | Jordan derivation | Left Jordan derivation | MATHEMATICS | IDENTITIES | left Jordan derivation | left derivation | MAPPINGS | derivation | JORDAN DERIVATIONS | semiprime ring

Integers | Commutativity | Mathematical theorems | Algebra | Logical proofs | Mathematical rings | Polynomials | Commuting | Linearization | Prime ring | (m, n)-Jordan derivation | Semiprime ring | Derivation | Left derivation | Jordan derivation | Left Jordan derivation | MATHEMATICS | IDENTITIES | left Jordan derivation | left derivation | MAPPINGS | derivation | JORDAN DERIVATIONS | semiprime ring

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 12/2007, Volume 11, Issue 5, pp. 1431 - 1441

In this paper we prove the following result: Let R be a prime ring of characteristic different from two and let T : R → R be an additive mapping satisfying the...

Homomorphisms | Algebra | Logical proofs | Quotients | Mathematical rings | Polynomials | Linearization | Functional identity | Prime ring | Two-sided centralizer | Left (right) centralizer | Semiprime ring | MATHEMATICS | left (right) centralizer | D-FREE SUBSETS | two-sided centralizer | JORDAN DERIVATIONS | semiprime ring | functional identity | prime ring | FUNCTIONAL IDENTITIES

Homomorphisms | Algebra | Logical proofs | Quotients | Mathematical rings | Polynomials | Linearization | Functional identity | Prime ring | Two-sided centralizer | Left (right) centralizer | Semiprime ring | MATHEMATICS | left (right) centralizer | D-FREE SUBSETS | two-sided centralizer | JORDAN DERIVATIONS | semiprime ring | functional identity | prime ring | FUNCTIONAL IDENTITIES

Journal Article

数学学报：英文版, ISSN 1439-8516, 2010, Volume 26, Issue 8, pp. 1555 - 1566

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 12/2007, Volume 11, Issue 5, pp. 1383 - 1395

In this paper we describe superderivations in certain superalgebras by their actions on elements satisfying some special conditions. One of the main results is...

Linear transformations | Centroids | Mathematical rings | Algebra | Automorphisms | Superderivations | Local superderivations | Superalgebras | superderivations | MATHEMATICS | superalgebras | AUTOMORPHISMS | local superderivations | NEST-ALGEBRAS | DERIVATIONS

Linear transformations | Centroids | Mathematical rings | Algebra | Automorphisms | Superderivations | Local superderivations | Superalgebras | superderivations | MATHEMATICS | superalgebras | AUTOMORPHISMS | local superderivations | NEST-ALGEBRAS | DERIVATIONS

Journal Article

Glasnik Matematicki, ISSN 0017-095X, 2018, Volume 53, Issue 1, pp. 73 - 95

A classical result of Herstein asserts that any Jordan derivation on a prime ring of characteristic different from two is a derivation. It is our aim in this...

Functional identity | Prime ring | Derivation | Jordan derivation | Semiprime ring | MATHEMATICS | MATHEMATICS, APPLIED | SEMIPRIME RINGS | derivation | JORDAN DERIVATIONS | STANDARD OPERATOR-ALGEBRAS | semiprime ring | functional identity | PRIME-RINGS

Functional identity | Prime ring | Derivation | Jordan derivation | Semiprime ring | MATHEMATICS | MATHEMATICS, APPLIED | SEMIPRIME RINGS | derivation | JORDAN DERIVATIONS | STANDARD OPERATOR-ALGEBRAS | semiprime ring | functional identity | PRIME-RINGS

Journal Article

Glasnik Matematicki, ISSN 0017-095X, 2011, Volume 46, Issue 2, pp. 339 - 349

In this paper we investigate identities with derivations in rings. We prove, for example the following result. Let m >= in >= 1 be some fixed integers and let...

Prime ring | Derivation | Semiprime ring | MATHEMATICS | MATHEMATICS, APPLIED | derivation | SEMIPRIME RINGS | semiprime ring

Prime ring | Derivation | Semiprime ring | MATHEMATICS | MATHEMATICS, APPLIED | derivation | SEMIPRIME RINGS | semiprime ring

Journal Article

Glasnik Matematicki, ISSN 0017-095X, 2011, Volume 46, Issue 1, pp. 31 - 41

In this paper we prove the following result. Let m >= 0 and n >= 0 be integers with m + n not equal 0 and let R be a prime ring with char(R) = 0 or m + n + 1...

Functional identity | Prime ring | Derivation | MATHEMATICS | MATHEMATICS, APPLIED | derivation | CENTRALIZING MAPPINGS | functional identity | FUNCTIONAL IDENTITIES

Functional identity | Prime ring | Derivation | MATHEMATICS | MATHEMATICS, APPLIED | derivation | CENTRALIZING MAPPINGS | functional identity | FUNCTIONAL IDENTITIES

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 11/2012, Volume 9, Issue 4, pp. 847 - 863

In this paper we investigate identities with two generalized derivations in prime rings. We prove, for example, the following result. Let R be a prime ring of...

Prime ring | Mathematics, general | Mathematics | derivation | semiprime ring | generalized derivation | 16N60 | MATHEMATICS | MATHEMATICS, APPLIED | JORDAN DERIVATIONS

Prime ring | Mathematics, general | Mathematics | derivation | semiprime ring | generalized derivation | 16N60 | MATHEMATICS | MATHEMATICS, APPLIED | JORDAN DERIVATIONS

Journal Article

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