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...

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...

applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect product of "simpler" algebras. Subdirectly irreducible...

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...

generalizes the semidirect product Holomorph Lie algebra semidirect sum Subdirect product Wreath product Zappa–Szép product Crossed product DS Dummit and RM Foote...

{\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...

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...

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...

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...

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...