Commutation with skew elements in rings with involution

Lanski, Charles

doi:10.2140/pjm.1979.83.393

Cited by 10 publications

(4 citation statements)

References 9 publications

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“…There has been a considerable interest on the behaviour of derivations and commutativity of rings during the last few decades ( see [1], [6], [9], [13]). The notion of rings with involution was first introduced by Herstein [9] and thereafter the algebraic structure rings with involution carried much importance in ring theory (see [3], [11], [12]). In 1998, Beidar and Martindale [5] examined some functional identities in prime rings with involution.…”

Section: Introductionmentioning

confidence: 99%

A study on derivations of inverse semirings with involution

Dadhwal,

Devi

2024

Proyecciones (Antofagasta)

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In this research article, we study the influence of derivations on semirings with involution which resembles with commutativity preserving mappings. The action of derivations on Lie ideals and some differential identities regarding Lie ideals are also investigated. It is proved that for any two derivations d1, d2 of a prime semiring S with involution ⋆ such that atleast one of d1, d2 is nonzero and char(S) 2, then the identity [d1(a), d2(a ⋆ )] + d2(a ◦ a ⋆ ) = 0, for all a ∈ L implies [L , S] = (0), where L is a Lie ideal of S.

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Section: Introductionmentioning

confidence: 99%

A study on derivations of inverse semirings with involution

Dadhwal,

Devi

2024

Proyecciones (Antofagasta)

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“…Involution plays a vital role in defining the important structures like B*-algebra and C*algebra. The rings with involution are also investigated by many algebraists (see (1)(2)(3)(4)(5) ). The concept of involution was also discussed for some other types inverse semirings (see (6)(7)(8)(9) ).…”

Section: Introductionmentioning

confidence: 99%

Some results on commutativity of MA-semirings

Ali¹

2020

IJST

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Objective: The main aim of this article is to extend the concept of involution for a certain class of semirings known as MA-semirings. Now a days the commutativity conditions in the theory of rings and semirings becomes crucial for researchers. This motivates us to discuss some conditions on MA-semirings with involution which enforces commutativity. Method: We use the tools of derivations and involutions of second kind on MA-semirings. Findings: We are able to find the conditions of commutativity in semirings through these particular mappings. Novelty: To define the concept of Hermitian elements in MA-semirings with involution and to establish some commutativity results through different conditions involving Hermitian elements is the novel idea.

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“…In literature, usually a self-inverse antiautomorphism for a given algebraic system is referred as involution [1][2][3][4][5][6]. It is worthy to be noted that the study of semirings with involution was also focussed by many authors in di_erent aspects.…”

Section: Introductionmentioning

confidence: 99%

On Jordan Ideals of Inverse Semirings with Involution

Ali¹

2020

IJST

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Objectives:The main objective of this article is to introduce *-Jordan ideals of a certain class of semirings called MA-semirings with involution and to investigate some conditions for which the above said ideals contained in the center. Methods and findings: We use the Jacobian identities and 2-torsion freeness of MA semirings. In this connection, we establish some important results of ring theory for the class of MA-semirings. Applications/ improvements: The commutative property is helpful to study the theory of semirings with ease therefore we find some conditions to impose commutativity in semirings, which are indeed novel idea in the field of semirings. Furthermore, these conditions are used in a most generalized way that these conditions bring the *-Jordan ideals to the center, therefore, it would be the corollary of result that semiring is commutative.

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Commutation with skew elements in rings with involution

Cited by 10 publications

References 9 publications

A study on derivations of inverse semirings with involution

A study on derivations of inverse semirings with involution

Some results on commutativity of MA-semirings

On Jordan Ideals of Inverse Semirings with Involution

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