rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: DIFFERENTIAL IDENTITIES IN RINGS AND ALGEBRAS AND THEIR APPLICATIONS
  name:
    name part: Ali, Shakir
    name part: 1971-
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Ashraf, Mohammad
    name part: 1959-
    role:
      role term: author.
  name:
    name part: Filippis, Vincenzo de
    name part: (Associate professor of algebra)
    role:
      role term: author.
  name:
    name part: Oukhtite, Lahchen
    name part: 1970-
    role:
      role term: author.
  name:
    name part: Rehman, Nadeem ur
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    place:
      place term: BOCA RATON
    publisher: CRC PRESS
    date issued: 2025
    edition: 1ST ED.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: "This outstanding research monograph deals with the nuances of a revolutionary concept of differential identities, which originated with the advent of derivations. The notion of derivation was introduced in rings as an additive map satisfying the Leibnitz rule. In an algebra, the condition of additivity translates to that of linearity. The operations of differentiation on a polynomial ring F[x], with F a field, is a natural example to begin with. In the study of derivations, inner derivations play a pivotal role, that assigns a commutator associated with a single fixed element to each element, i.e., x maps to [a,x]. Inner derivation may sometimes be the only possible derivation on rings or algebras. Among classical algebraic concepts, differential identity seems to be the closest one to the concept of a functional identity and with the advent of the twenty-first century the theory of differential identities has got a tremendous application in solving several outstanding problems in the theory of rings. Coming up with interesting results, the note Differential identities in rings and algebras with applications provides various contexts in which derivations are defined. Though the notion of derivations is quite old, it is still relevant in modern-day math. Posner's breakthrough revolutionized the study of derivations, by relating derivation to that of the structure of rings and algebras. Putting it differently, Posner opened up a door to several new and exciting results, mostly done on prime and semiprime rings. The theory of derivation was taken forward by various stalwarts like Beidar, Bell, Bergen, Bresar, Herstein, Hvala, Lanski, Lee, Luh, Kharchenko, Martindale, Vukman-to mention a few only. They have been keen to emphasize the applicability of derivations in each of their results. No wonder derivation finds its place in the applications of Coding theory, Cryptography, Information science, Field theory, Lie algebras, Linear differential equations, and the list go…
  table of contents: Preliminaries -- Derivations in rings and algebras -- Derivations on rings with involution -- Generalized derivations in rings -- Higher derivations in rings and algebras -- Applications of derivations.
  note: Includes bibliographical references and index.
  subject:
    topic: Differential algebra
  subject:
    topic: Rings (Algebra)
  subject:
    topic: Algèbre différentielle
  subject:
    topic: Anneaux (Algèbre)
  classification: QA247.4
  classification: 512/.56
  identifier: 1003504574
  identifier: 9781003504573
  identifier: 9781040370650
  identifier: 1040370659
  identifier: 9781040370605
  identifier: 1040370608
  identifier: 9781003504573 Taylor & Francis
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: YDX
    record creation date: 250119
    record change date: 20250620150215.7
    record identifier: in00005647481
    language of cataloging:
      language term: eng