Model theoretic properties in the variety generated by a primal algebra

1993 ◽  
Vol 30 (4) ◽  
pp. 526-537
Author(s):  
G. C. Nelson
Keyword(s):  
Primal Algebra

Maximal Pre-Primal Clusters

1975 ◽  
Vol 27 (4) ◽  
pp. 746-751
Author(s):  
Jon Froemke
Keyword(s):  
Primal Algebra ◽  
Algebra Theory

A number of unsolved problems of primal algebra theory concern the existence of certain collections of dependent primal algebras. In [3] E. S. O'Keefe showed that any collection of pairwise non-isomorphic primal algebras of type {n} with n > 1 forms a primal cluster. Recently the author has discovered that if τ is any type containing at least two elements, one of which is > 1, then there are at least two non-isomorphic dependent primal algebras of type τ, except possibly in the case = {2, 0}; this result will appear later.

scholarly journals The spectrum of a lattice-primal algebra

1981 ◽  
Vol 35 (1-3) ◽  
pp. 157-163 ◽  
Author(s):  
R. Mckenzie ◽  
R. Quackenbush
Keyword(s):  
Primal Algebra

scholarly journals n-Permutability is not join-prime for n ≥ 5

2020 ◽  
Vol 30 (08) ◽  
pp. 1717-1737
Author(s):  
Gergő Gyenizse ◽  
Miklós Maróti ◽  
László Zádori
Keyword(s):  
Primal Algebra ◽  
Bounded Poset ◽  
Finite Set ◽  
Near Unanimity

Let [Formula: see text] be the variety generated by an order primal algebra of finite signature associated with a finite bounded poset [Formula: see text] that admits a near-unanimity operation. Let [Formula: see text] be a finite set of linear identities that does not interpret in [Formula: see text]. Let [Formula: see text] be the variety defined by [Formula: see text]. We prove that [Formula: see text] is [Formula: see text]-permutable for some [Formula: see text]. This implies that there is an [Formula: see text] such that [Formula: see text]-permutability is not join-prime in the lattice of interpretability types of varieties. In fact, it follows that [Formula: see text]-permutability where [Formula: see text] runs through the integers greater than 1 is not prime in the lattice of interpretability types of varieties. We strengthen this result by making [Formula: see text] and [Formula: see text] more special. We let [Formula: see text] be the 6-element bounded poset that is not a lattice and [Formula: see text] the variety defined by the set of majority identities for a ternary operational symbol [Formula: see text]. We prove in this case that [Formula: see text] is 5-permutable. This implies that [Formula: see text]-permutability is not join-prime in the lattice of interpretability types of varieties whenever [Formula: see text]. We also provide an example demonstrating that [Formula: see text] is not 4-permutable.

Stone duality for primal algebra theory

1969 ◽  
Vol 110 (3) ◽  
pp. 180-198 ◽  
Author(s):  
Tah-Kai Hu
Keyword(s):  
Stone Duality ◽  
Primal Algebra ◽  
Algebra Theory
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