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algebra universalis

, Volume 46, Issue 1–2, pp 253–283 | Cite as

Finite-to-finite universal quasivarieties are Q-universal

  • M. E. Adams
  • W. Dziobiak

Abstract.

Let K be a quasivariety of algebraic systems of finite type. K is said to be universal if the category G of all directed graphs is isomorphic to a full subcategory of K. If an embedding of G may be effected by a functor F:G \( \longrightarrow \) K which assigns a finite algebraic system to each finite graph, then K is said to be finite-to-finite universal. K is said to be Q-universal if, for any quasivariety M of finite type, L(M) is a homomorphic image of a sublattice of L(K), where L(M) and L(K) are the lattices of quasivarieties contained in M and K, respectively.¶We establish a connection between these two, apparently unrelated, notions by showing that if K is finite-to-finite universal, then K is Q-universal. Using this connection a number of quasivarieties are shown to be Q-universal.

Key words: Quasivariety, variety, lattice of quasivarieties, universal category, Q-universal, graph. 

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Copyright information

© Birkhäuser Verlag Basel, 2001

Authors and Affiliations

  • M. E. Adams
    • 1
  • W. Dziobiak
    • 2
  1. 1.Department of Mathematics, State University of New York, New Paltz, NY 12561, e-mail: adamsm@matrix.newpaltz.eduUS
  2. 2.Department of Mathematics, University of Puerto Rico, Mayagüez, PR 00681-5000, e-mail: dziobiak@math.uprm.eduPR

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