Modular varieties with the Fraser-Horn property

Vaggione, Diego

doi:10.1090/S0002-9939-99-04647-X

Modular varieties with the Fraser-Horn property
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Proc. Amer. Math. Soc. 127 (1999), 701-708 Request permission

Abstract:

The notion of central idempotent elements in a ring can be easily generalized to the setting of any variety with the property that proper subalgebras are always nontrivial. We will prove that if such a variety is also congruence modular, then it has factorable congruences, i.e., it has the Fraser-Horn property. (This property is well known to have major implications for the structure theory of the algebras in the variety.)

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