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GCD ring
Redirected from "GCD rings".
Contents
Context
Algebra
- algebra, higher algebra
- universal algebra
- monoid, semigroup, quasigroup
- nonassociative algebra
- associative unital algebra
- commutative algebra
- Lie algebra, Jordan algebra
- Leibniz algebra, pre-Lie algebra
- Poisson algebra, Frobenius algebra
- lattice, frame, quantale
- Boolean ring, Heyting algebra
- commutator, center
- monad, comonad
- distributive law
Group theory
Ring theory
Module theory
Contents
Definition
Given a commutative monoid , we say that element divides () if there exists an element such that .
Given a commutative ring , let be the multiplicative submonoid of regular elements in .
Definition
A commutative ring is a GCD ring if for every element and , there is an element such that and , and for every other element such that and , .
See also
References
Last revised on August 19, 2024 at 15:04:53.
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