# subring

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**Subring**— In mathematics, a subring is a subset of a ring, which contains the multiplicative identity and is itself a ring under the same binary operations. Naturally, those authors who do not require rings to contain a multiplicative identity do not… … Wikipedia**subring**— noun Date: 1937 a subset of a mathematical ring which is itself a ring … New Collegiate Dictionary**subring**— /sub ring /, n. Math. a subset of a ring that is a subgroup under addition and that is closed under multiplication. Cf. ring1 (def. 22). [1950 55; SUB + RING1] * * * … Universalium**subring**— sub·ring … English syllables**subring**— ˌ noun Etymology: sub + ring (I) : a subset of a mathematical ring which is itself a ring * * * /sub ring /, n. Math. a subset of a ring that is a subgroup under addition and that is closed under multiplication. Cf. ring1 (def. 22). [1950 55; SUB … Useful english dictionary**Subring test**— In abstract algebra, the subring test is a theorem that states that for any ring, a nonempty subset of that ring is a subring if it is closed under multiplication and subtraction. Note that here that the terms ring and subring are used without… … Wikipedia**Ring (mathematics)**— This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… … Wikipedia**Integrality**— In commutative algebra, the notions of an element integral over a ring (also called an algebraic integer over the ring), and of an integral extension of rings, are a generalization of the notions in field theory of an element being algebraic over … Wikipedia**Depth of noncommutative subrings**— In ring theory and Frobenius algebra extensions, fields of mathematics, there is a notion of depth two subring or depth of a Frobenius extension. The notion of depth two is important in a certain noncommutative Galois theory, which generates Hopf … Wikipedia**Cayley–Hamilton theorem**— In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Hamilton) states that every square matrix over the real or complex field satisfies its own characteristic equation.More precisely; if A is… … Wikipedia