as universal algebra (and in its applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect product of "simpler"...
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direct (subdirect) representation of an algebra A is a direct (subdirect) product isomorphic to A. An algebra is called subdirectly irreducible if it is...
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field. In abstract algebra, irreducible can be an abbreviation for irreducible element of an integral domain; for example an irreducible polynomial. In representation...
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(and forms another Heyting algebra) is subdirectly irreducible, whence every Heyting algebra can be made subdirectly irreducible by adjoining a new greatest...
44 KB (6,294 words) - 04:58, 1 May 2025
reducible" and "subdirectly reducible" are used when a ring is not meet-irreducible, or not directly irreducible, or not subdirectly irreducible, respectively...
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only if A(X) is finitely subdirectly irreducible X is compact ultra-connected if and only if A(X) is subdirectly irreducible The modern formulation of...
30 KB (3,849 words) - 16:33, 14 June 2025
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 distributive...
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Noncommutative ring (redirect from Noncommutative algebra)
noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted to study of properties of the noncommutative...
20 KB (2,804 words) - 01:41, 1 November 2023
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 a finite...
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Projective space (redirect from Projective space over a division algebra)
correspondence between projective spaces and geomodular lattices, namely, subdirectly irreducible, compactly generated, complemented, modular lattices. Dimension...
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286–295. doi:10.1080/00029890.1942.11991226. McCoy, Neal H. (1945). "Subdirectly irreducible commutative rings". Duke Mathematical Journal. 12 (2). doi:10...
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Thompson, Nick. "Irreducible Brillouin Zones and Band Structures". bandgap.io. Retrieved 13 December 2017.[dead link] "abstract algebra - Can every non-simple...
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daughter, and four grandchildren. Zitarelli, David E. (1977). "Subdirectly irreducible Rees matrix semigroups". Bulletin of the Australian Mathematical...
13 KB (1,350 words) - 13:55, 23 May 2025