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...

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...

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

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...

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...

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...

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...

just a semisimple ring. Semiprimitive rings can be understood as subdirect products of primitive rings, which are described by the Jacobson density theorem...

following linear subdirect decomposition property: Every MTL-algebra is a subdirect product of linearly ordered MTL-algebras. (A subdirect product is a subalgebra...

and 0 {\displaystyle 0} otherwise. Every skew Boolean algebra is a subdirect product of primitive algebras. Skew Boolean algebras play an important role...

direct product (of copies) of the canonical L n {\displaystyle {\mathcal {L}}_{n}} algebra. As a corollary, every LMn algebra is a subdirect product of subalgebras...

{2}})} ). More generally the real closure of a field F is a certain subdirect product of the real closures of the ordered fields (F,P), where P runs through...

pp. 167–168. ISBN 978-981-277-688-4. preprint Mitsch, H. (2009). "Subdirect products of E–inversive semigroups". Journal of the Australian Mathematical...

structure as a composition of simpler structures using a product construction; for example subdirectly irreducible. A 3-manifold is P²-irreducible if it is...

subgroups). More is true: the Prüfer p-groups are subdirectly irreducible. An abelian group is subdirectly irreducible if and only if it is isomorphic to...

ISBN 0-521-78451-4, 10.23 Infinite distributive laws, pp. 239–240 G. N. Raney, A subdirect-union representation for completely distributive complete lattices, Proceedings...

(and forms another Heyting algebra) is subdirectly irreducible, whence every Heyting algebra can be made subdirectly irreducible by adjoining a new greatest...

correspondence between projective spaces and geomodular lattices, namely, subdirectly irreducible, compactly generated, complemented, modular lattices. Dimension...