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Subdirectly irreducible algebra
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Subdirectly irreducible algebra : ウィキペディア英語版
Subdirectly irreducible algebra
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.
==Definition==
A universal algebra ''A'' is said to be subdirectly irreducible when ''A'' has more than one element, and when any subdirect representation of ''A'' includes (as a factor) an algebra isomorphic to ''A'', with the isomorphism being given by the projection map.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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