- is used in this article), the only
ideal of R that is a
subring of R is R itself. A
subring of a ring (R, +, ∗, 0, 1) is a
subset S of R that preserves...
-
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...
- {\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...
-
Southern University and A&M
College (Southern University, Southern,
SUBR or SU) is a
public historically black land-grant
university in
Baton Rouge, Louisiana...
- 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 ****ociative
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,...
-
tower of
iterated endomorphism rings above the
subring. A more
recent definition of
depth of any
unital subring in any ****ociative ring is
proposed (see below)...
- In algebra, the fixed-point
subring Rf{\displaystyle R^{f}} of an
automorphism f of a ring R is the
subring of the
fixed points of f, that is, Rf={r∈R∣f(r)=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...
- Artinian, Noetherian, prime. If S is a
subring of R, then Mn(S) is a
subring of Mn(R). For example, Mn(Z) is a
subring of Mn(Q). The
matrix ring Mn(R) is...
