group theory, ring theory, and module theory, a subdirect product is a subalgebra of a direct product that depends fully on all its factors without however...
4 KB (558 words) - 01:02, 3 May 2020
lemma, every subdirect product is a fiber product. Let G, H, and Q be groups, and let 𝜑: G → Q and χ: H → Q be homomorphisms. The fiber product of G and...
26 KB (2,932 words) - 23:03, 19 April 2024
only if it is a subdirect product of left primitive rings. A commutative ring is semiprimitive if and only if it is a subdirect product of fields, (Lam...
3 KB (372 words) - 18:27, 14 June 2022
applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect product of "simpler" algebras. Subdirectly irreducible...
6 KB (853 words) - 15:09, 18 October 2023
generalizes the semidirect product Holomorph Lie algebra semidirect sum Subdirect product Wreath product Zappa–Szép product Crossed product DS Dummit and RM Foote...
30 KB (4,541 words) - 06:25, 10 August 2024
that every distributive lattice is a subdirect product of copies of the two-element chain, or that the only subdirectly irreducible member of the class of...
17 KB (2,053 words) - 23:54, 16 May 2024
rings are unit regular. Every strongly von Neumann regular ring is a subdirect product of division rings. In some sense, this more closely mimics the properties...
10 KB (1,305 words) - 01:22, 25 November 2023
{\displaystyle p_{2}:H\to G'} are surjective (i.e., H {\displaystyle H} is a subdirect product of G {\displaystyle G} and G ′ {\displaystyle G'} ). Let N {\displaystyle...
7 KB (1,511 words) - 23:04, 18 January 2024
A_{12})\rtimes \mathbb {Z} _{2}).} This group can also be described as the subdirect product [ ( Z 3 7 ⋊ S 8 ) × ( Z 2 11 ⋊ S 12 ) ] 1 2 {\displaystyle [(\mathbb...
14 KB (2,044 words) - 05:11, 6 July 2024
is subdirectly irreducible; when R is written as a subdirect product of rings, then one of the projections of R onto a ring in the subdirect product is...
4 KB (564 words) - 19:58, 20 August 2023