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.
Other articles related to "subdirectly irreducible algebra, algebra, subdirectly irreducible, irreducibles":
... A necessary and sufficient condition for a Heyting algebra to be subdirectly irreducible is for there to be a greatest element strictly below 1 ... chain of two or more elements as a Heyting algebra is subdirectly irreducible ... By Jónsson's Lemma the subdirect irreducibles of the variety generated by a class of subdirect irreducibles are no larger than the generating subdirect ...
Famous quotes containing the words algebra and/or irreducible:
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (18831955)
“If an irreducible distinction between theatre and cinema does exist, it may be this: Theatre is confined to a logical or continuous use of space. Cinema ... has access to an alogical or discontinuous use of space.”
—Susan Sontag (b. 1933)