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• Ring
  ...is commutative making it an Abelian one at that), that is a ring is just a group {{M|(G,+)}} with another operation on {{M|G}} called {{M|\times}} * [[Direct sum (ring)|Direct sum of rings]]
  7 KB (1,248 words) - 05:02, 16 October 2016
• Direct sum (ring)
  For other kinds of ''direct sums'' see [[Direct sum]] ...g|rings]] {{M|(R,+_R,\times_R)}} and {{M|(S,+_S,\times_S)}} their ''direct sum'' is defined on the set {{M|R\times S}} (where {{M|\times}} is the [[Cartes
  3 KB (549 words) - 14:32, 8 June 2015
• Direct sum
  * [[Direct sum (ring)|Direct sum of rings]] * [[Direct sum (group)|Direct sum of groups]]
  172 B (25 words) - 14:04, 17 June 2015
• Module
  Let {{M|(R,+,*,0)}}<ref group="Note">Or {{M|(R,+,*,0,1)}} if the ring has unity. Standard notation</ref> * An [[Abelian group]], {{M|(M,\oplus)}} together with a
  1 KB (246 words) - 22:40, 19 October 2016
• Direct product module
  ...}M_\alpha}} for convenience). This is a standard [[Cartesian product]]<ref group="Note">An alternate construction is that {{M|\prod_{\alpha\in I}M_\alpha}} *# ''Addition: ''<ref group="Note">the operation of the [[Abelian group]] that makes up a module</ref> {{M|+:M\times M\rightarrow M}} by {{M|+:((x_
  3 KB (431 words) - 22:19, 19 October 2016
• For any vector subspace of a Hilbert space the orthogonal complement and the closure of that subspace form a direct sum of the entire space
  ...mplement]] of {{M|L}} - is a (topologically) [[closed set]] of {{M|X}}<ref group="Note">With {{M|X}} considered with the [[topology induced by the metric]] ...topology}} of a set {{M|A\in\mathcal{P}(X)}} and {{M|\oplus}} the [[direct sum of vector spaces]]
  3 KB (633 words) - 04:07, 8 April 2017