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On the structure of semilattice sums. (English) Zbl 0793.08010
This paper investigates the structure of algebras of given type \(\tau: \Omega\to N\) in regular classes and in particular in regular classes of modes [see the authors: Modal theory. An algebraic approach to order, geometry, and convexity (1985; Zbl 0553.08001)]. Recall that an identity is regular if the sets of variables appearing on each side are equal. A class \({\mathcal V}\) of algebras of type \(\tau: \Omega\to N\) is regular if the only identities satisfied by all algebras in \({\mathcal V}\) are regular. Otherwise, \({\mathcal V}\) is irregular. The algebras considered in this paper are of type \(\tau: \Omega\to \mathbb{Z}^ +\) with \(2\in \tau(\Omega)\).

08C99 Other classes of algebras
06A12 Semilattices
08B99 Varieties
08B25 Products, amalgamated products, and other kinds of limits and colimits
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