In the branch of mathematics known as universal algebra (and in its applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect product of "simpler" algebras. Subdirectly irreducible algebras play a somewhat analogous role in algebra to primes in number theory.
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as universal algebra (and in its applications), a subdirectlyirreduciblealgebra is an algebra that cannot be factored as a subdirect product of "simpler"...
(and forms another Heyting algebra) is subdirectlyirreducible, whence every Heyting algebra can be made subdirectlyirreducible by adjoining a new greatest...
direct (subdirect) representation of an algebra A is a direct (subdirect) product isomorphic to A. An algebra is called subdirectlyirreducible if it is...
only if A(X) is finitely subdirectlyirreducible X is compact ultra-connected if and only if A(X) is subdirectlyirreducible The modern formulation of...
reducible" and "subdirectly reducible" are used when a ring is not meet-irreducible, or not directly irreducible, or not subdirectlyirreducible, respectively...
every distributive lattice is a subdirect product of copies of the two-element chain, or that the only subdirectlyirreducible member of the class of distributive...
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...
2016-03-07. Thompson, Nick. "Irreducible Brillouin Zones and Band Structures". bandgap.io. Retrieved 13 December 2017. "abstract algebra - Can every non-simple...
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