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algebra over a ring
(algebra) A module (over some ring) with an additional binary operation, a module-element-valued product between module elements, which is bilinear over module addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the module multiplication with respect to the module addition, which means that such a module is also a ring.)
algebra over a field
(algebra) A vector space (over some field) with an additional binary operation, a vector-valued product between vectors, which is bilinear over vector addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the vector multiplication with respect to the vector addition, which means that such a vector space is also a ring.)
numerical linear algebra
(computing) The study of numerical analysis algorithms to solve mathematical problems in the field of linear algebra.
algebraic graph theories
algebraic graph theory
(uncountable, mathematics, graph theory) The subbranch of graph theory in which algebraic methods are applied to problems about graphs.
algebraic K-theory
algebraic fundamental groups
algebraic fundamental group
(algebraic geometry) A group which is an analogue for schemes of the fundamental group for topological spaces.