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The partially ordered monoid generated by the operators H, S, P u , P f on classes of algebras

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Abstract

Let I, H, S, P u , P f denote the following operators on classes of algebras of the same type: I, H for isomorphic and homomorphic images of algebras, S for subalgebras and P u , P f for ultra and filtered products, respectively. In this paper, the monoid generated by the operators H, S, P u , P f with I as an identity is described. It turns out that there are 44 different operators such that every composite of H, S, P u , P f coincides with one of them (including the empty composite, the identity operator).

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Authors and Affiliations

  1. Department of Mathematics, Ryerson University, 350 Victoria Street, Toronto, Ontario, N5B 2K3, Canada

    Boža Tasić

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  1. Boža Tasić
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Correspondence to Boža Tasić.

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Presented by K. Kearnes.

This article is dedicated to Alexandre Schnubb

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Tasić, B. The partially ordered monoid generated by the operators H, S, P u , P f on classes of algebras. Algebra Univers. 62, 351–365 (2009). https://doi.org/10.1007/s00012-010-0046-7

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