Topological Rings and Infinite Matrices |
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Page 2
... subring of the ring of homomorphisms of the additive group of the ring into itself . Using known properties of compact commutative groups and our direct sum decomposition we are able to conclude something of the structure of compact ...
... subring of the ring of homomorphisms of the additive group of the ring into itself . Using known properties of compact commutative groups and our direct sum decomposition we are able to conclude something of the structure of compact ...
Page 29
... subring R such that G is R operator homomorphic to R , then multiplication may be defined in G so that G is a topological ring and is ring homomorphic to R. Proof : This is an immediate consequence of the corresponding theorem of 29 .
... subring R such that G is R operator homomorphic to R , then multiplication may be defined in G so that G is a topological ring and is ring homomorphic to R. Proof : This is an immediate consequence of the corresponding theorem of 29 .
Page 38
... subring of C ( H , H ) . However , we may also note that multiplication in H defines not merely a homomorphism , but an R operator homomorph- ism , hence , H is homomorphic to a subring of O ( H , H , R , R ) , that is , H is ...
... subring of C ( H , H ) . However , we may also note that multiplication in H defines not merely a homomorphism , but an R operator homomorph- ism , hence , H is homomorphic to a subring of O ( H , H , R , R ) , that is , H is ...
Common terms and phrases
abelian topological group addition and multiplication additive group axiom of countability bourhood columns compact and satisfy compact commutative group continuous function correspondence is continuous correspondence is preserved countability axiom countable set d₂ defined definition 2.9 denote exists a neighbourhood finitely non-zero rows form a basis G into G G₂ give all possible group with operator Hausdorff space infinite basis infinite direct sum infinite matrices infinitely non-zero integers inuous lemma Let G linear subspace linear transformations matrix theory neigh neighbourhood of zero neighbourhoods in G non-singular matrices noted open set operator homomorph operator ring possible orders preserved under addition principal diagonal principal ideal ring Proof real numbers ring of homomorphisms ring of infinite ring of matrices ring of operators Rings and Infinite satisfying the second second axiom sequence subring Suppose lim theorem 4.1 theory of infinite thesis topological ring U₂ University of Wisconsin vector space whence