intersection of subrings of R is itself a subring of R; therefore, the subring generated by X (denoted here as S) is indeed a subring of R. This subring S is the...

{\displaystyle x} . If A is a subring of a ring B, and b is an element of B, then A[b] denotes the subring of B generated by A and b. This subring consists of all the...

intersection of subrings is a subring. Given a subset E of R, the smallest subring of R containing E is the intersection of all subrings of R containing E, and...

Southern University and A&M College (Southern University, Southern, SUBR or SU) is a public historically black land-grant university in Baton Rouge, Louisiana...

tower of iterated endomorphism rings above the subring. A more recent definition of depth of any unital subring in any associative ring is proposed (see below)...

to R. The characteristic is the natural number n such that R contains a subring isomorphic to the factor ring Z / n Z {\displaystyle \mathbb {Z} /n\mathbb...

Conversely, if R is an associative algebra over a commutative subring S, then S is a subring of the center of R, and if S happens to be the center of R,...

R be a ring. Let S be a subring of R, and let I be an ideal of R. Then: The sum S + I = {s + i | s ∈ S, i ∈ I } is a subring of R, The intersection S ∩ I...

In algebra, the fixed-point subring R f {\displaystyle R^{f}} of an automorphism f of a ring R is the subring of the fixed points of f, that is, R f =...

In mathematics, especially in the field of module theory, the concept of pure submodule provides a generalization of direct summand, a type of particularly...