An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.
A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
A universal algebra.
One of several other types of mathematical structure.
The study of algebraic structures.
The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
An algebra over a field; a ring with identity together with an injective ring homomorphism from a field, k, to the ring such that the image of the field is a subset of the center of the ring and such that the image of the field’s unity is the ring’s unity.