In other words, there is a ring homomorphism from the field into the endomorphism ring of the group of vectors.
12.
When the field is not algebraically closed, the case where the endomorphism ring is as small as possible is still of particular interest.
13.
Non-commutative local rings arise naturally as endomorphism rings in the study of length and is indecomposable, then its endomorphism ring is local.
14.
Non-commutative local rings arise naturally as endomorphism rings in the study of length and is indecomposable, then its endomorphism ring is local.
15.
More generally, endomorphism rings of abelian groups are rarely commutative, the simplest example being the endomorphism ring of the Klein four-group.
16.
More generally, endomorphism rings of abelian groups are rarely commutative, the simplest example being the endomorphism ring of the Klein four-group.
17.
Thus the category has unique decomposition into indecomposables, but is not Krull-Schmidt since the regular module does not have a local endomorphism ring.
18.
They express relations between the module-theoretic properties of " M " and the properties of the endomorphism ring of " M ".
19.
A simple module over " k "-algebra is said to be absolutely simple if its endomorphism ring is isomorphic to " k ".
20.
Then Schur's lemma says that the endomorphism ring of the module " M " is a division algebra over the field " k ".
