Residually Small Varieties Without Rank

Subdirect representations are investigated in varieties which are defined by operations of not necessarily finite arity. It is shown that, in this context, Birkhoff's Subdirect Representation Theorem does not hold. However, a class of unranked varieties is identified which admit subdirect representations by subdirectly irreducibles and then even are residually small.

• Type: Journal
• Year: 2004
• Where: ACS
• Authors: Hans-E. Porst
• Keywords: ACS 2004, ACS 2007, Arity, Subdirect Representation Theorem, Subdirect Representations