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algebra Definition

al·ge·bra (al′jə brə)

noun

  1. a mathematical system using symbols, esp. letters, to generalize certain arithmetic operations and relationships (Ex.: x + y = x represents a unique relationship between x and y, and has an infinite number of examples, as 3 + 6 = 9)
  2. any of various symbolic mathematical systems having formal rules of operation, defined relationships, finite processes, etc. Boolean algebra
  3. a textbook or treatise dealing with algebra

Etymology: ME < ML < Ar al-jabr, the reunion of broken parts < al, the + jabara, to reunite

algebra Related Forms
al′·ge·bra′·ist (-brā′ist) noun
algebra Usage Examples

Preposition: of

  • observables: Accordingly everything is expressed in terms of local algebras of observables.
  • matrix: Much of this work is based on the notion of a C* algebras, a natural abstraction of algebras of matrices.

Converse of object

  • envelop: In Chapter 2. we give a short summary of parts of the theory of quantized enveloping algebras.
  • associate: Current projects include: The structure of operator algebras associated with certain groups.
  • construct: Another approach is to construct algebras directly from the algebraic group itself.
  • teach: He has also developed TREEFROG - a software package to teach algebra at schools.

Adjective modifier

  • associative: We call a free associative algebra A over R a polynomial ring over R.
  • commutative: The method is similar in some respects to the treatment of non commutative algebras.
  • linear: Outline content: The module starts with review of linear algebra.
  • stochastic: Analysis of a multimedia stream using stochastic process algebra.
  • geometric: Geometric algebra can be applied to any subject in mathematics, physics or engineering which is in some part rooted in geometry.
  • topological: In the algebraic theory of data, continuous data types are modeled by topological algebras.

Modifies a noun

  • package: The basic toolbox also allows you to access functions in Maple's linear algebra package.
  • module: Soon we will be doing an algebra module from our scheme of work.

Noun used with modifier

  • quaternion: An error in the computation of inverses in quaternion algebras with non-standard parameters.
  • matrix: In addition: the authors include in an appendix a review of all relevant topics in matrix algebra.
  • vector: The vast majority of simulations of physical systems, including the movement of rigid bodies under forces, are carried out using vector algebra.
  • computer: Have strong linkage to the Maple computer algebra system.
  • operator: Current projects include: The structure of operator algebras associated with certain groups.
  • quantum: The counterexample is the quantum exterior algebra in 2 variables.