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.

Read more about Subdirectly Irreducible Algebra: Definition, Examples, Properties, Applications

### Other articles related to "subdirectly irreducible algebra, algebra, subdirectly irreducible, irreducibles":

**Subdirectly Irreducible Algebra**- Applications

... 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 ...

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