Sentence examples for matrix ring from inspiring English sources
Take (R = M_2 (mathbb {Z})), the (2 times 2) matrix ring over (mathbb {Z}).
The system designed as a matrix ring delivers 10 mg/day of the physiological hormone progesterone.
Any non-commutative ring R can be embedded in a matrix ring (mathbb {M}(l,K)) for some positive integer l.
By [50, Chapter 3], V ( R ) can be viewed as the set of equivalence classes V ( e ) of idempotents e in the (nonunital) infinite matrix ring M N ( R ), with operation V ( e ) + V ( f ) = V ( e 0 0 f ).
Therefore, the statement in Theorem 4.11 is also valid if we replace "commutative noetherian ring R" by "a full matrix ring (mathbb {M}_n(R)) over a commutative noetherian ring R".
In the rest of this paper, assume that R is realized as a subring of the matrix ring (mathbb {M}(s,L)) for some (sin mathbb {N}), and closed by the transpose operation.
Other examples include full matrix rings over division rings and triangular matrix rings over fields.
Finite matrix rings over commutative noetherian rings are a large class of right FBN rings which are not commutative.
As a consequence, passing to matrix rings is a functor on the category of AW*-algebras.
Full matrix rings over K arise as the Leavitt path algebras of graphs other than the A n graphs.
By construction we have R R ≅ R R n as left R -modules; so by taking endomorphism rings and using the standard representation of these endomorphism rings as matrix rings, we get R ≅ M n ( R ) as K -algebras.
