Algebra1. the abstract study of number systems and operations within them, including such advanced topics as groups, rings, invariant theory, and cohomology. = abstract algebra 2. a particular type of algebraic structure. Formally, an algebra is a vector space V over a field F with a multiplication, which is distributive, and for every f from F and every x,y from V
Etymology: from the title of a work written around 825 by the Arabic mathematician known as al-Khowarizmi, entitled al-jebr w' al-muqabalah. In Arabic, al- is the definite article "the." The first noun [Schwartzman, S. (2012). The Words of Mathematics: An Etymological Dictionary of Mathematical Terms used in English. Washington: The Mathematical Association of America.] | |
annihilatornoun Pronunciation: /ɐnˈaɪ.ə.leɪtə/ Definition: Let M be a left modul over a ring R and let S be a subset of M. The annihilator of S is the set of all r from R such that sr is equal to zero (for all s from S). Source: |
Associativitynoun Pronunciation: [ə,səʊsɪə'tɪvɪti] Meaning: a property of a binary operation; if it holds, then with more than one of the same operator, the order of operations does not matter Example: if + is an associative operator, then for every three elements a, b, c it holds that a + (b + c) = (a + b) + c Source: |