Assertion: algebra's set | /r/CapableOf | form ring
Facets:
value: with addition
type: OTHER
value: more generally
type: DEGREE
value: for any ring
type: TRANSITIVE-OBJECT
value: as operations
type: MANNER
value: with matrix multiplication
type: OTHER
Source sentences:
text: For any ring R and any natural number n , the set of all square n -by- n matrices with entries from R , forms a ring with matrix addition and matrix multiplication as operations.
text: More generally, if V is a left module over a ring R , then the set of all R -linear maps forms a ring, also called the endomorphism ring and denoted by End R ( V ).
text: More generally, if is a left module over a ring , then the set of all -linear maps forms a ring, also called the endomorphism ring and denoted by End ( ).
text: The set of all square matrices of size n with entries in R forms a ring with the entry-wise addition and the usual matrix multiplication.
text: Given a right R-module U {\displaystyle U} , the set of all R-linear maps from U to itself forms a ring with addition that is of function and multiplication that is of composition of functions; it is called the endomorphism ring of U and is denoted by End R ⁡ ( U ) {