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  • 11
    Electronic Resource
    Electronic Resource
    On Full and Faithful Kan Extensions (1998)
    Springer
    Applied categorical structures 6 (1998), S. 291-332 
    Details
    ISSN: 1572-9095
    Keywords: Kan extension ; factorization system ; full embedding ; universal category ; variety of algebras ; colimit of an α-directed diagram ; locally α-presentable category
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper introduces some mild requirements under which a Kan extension is a full embedding that preserves factorization systems and colimits of α-directed diagrams. The existence of such Kan extensions is then used to establish conditions equivalent to algebraic universality of concrete categories such as varieties of algebras of any given similarity type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008681922458
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  • 12
    Electronic Resource
    Electronic Resource
    Equimorphy in varieties of distributive double p-algebras (1998)
    Springer
    Czechoslovak mathematical journal 48 (1998), S. 473-544 
    Details
    ISSN: 1572-9141
    Keywords: distributive double p-algebra ; variety ; endomorphism monoid ; equimorphy ; categorical universality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Any finitely generated regular variety V of distributive double p-algebras is finitely determined, meaning that for some finite cardinal n(V), any subclass S $$ \subseteq $$ V of algebras with isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result follows from our structural characterization of those finitely generated almost regular varieties which are finitely determined. We conjecture that any finitely generated, finitely determined variety of distributive double p-algebras must be almost regular.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022479828440
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  • 13
    Electronic Resource
    Electronic Resource
    Minimal group-universal varieties of semigroups (1985)
    Springer
    Algebra universalis 21 (1985), S. 111-122 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01187561
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  • 14
    Electronic Resource
    Electronic Resource
    Finitely generated relatively universal varieties of Heyting algebras (1996)
    Springer
    Algebra universalis 35 (1996), S. 296-331 
    Details
    ISSN: 1420-8911
    Keywords: variety of Heyting algebras ; almost universal category ; Priestley's duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given distinct varieties $$\mathbb{V}$$ and $$\mathbb{W}$$ of the same type, we say that $$\mathbb{V}$$ is relatively $$\mathbb{W}$$ -universal if there exists an embedding Φ:K→ $$\mathbb{V}$$ from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:ΦA → ΦB has the formf=Φg for someK-morphismg:A →B if and only if Im(f) ∉ $$\mathbb{W}$$ . Finitely generated relatively $$\mathbb{W}$$ -universal varieties of Heyting algebras are described for the variety $$\mathbb{W}$$ of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195502
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  • 15
    Electronic Resource
    Electronic Resource
    Quotients of rigid (0,1)-lattices (1985)
    Springer
    Archiv der Mathematik 44 (1985), S. 403-412 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229322
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  • 16
    Electronic Resource
    Electronic Resource
    Full embeddability into categories of generalized algebras (1983)
    Springer
    Algebra universalis 17 (1983), S. 1-20 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194510
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  • 17
    Electronic Resource
    Electronic Resource
    Almost universal varieties of monoids (1984)
    Springer
    Algebra universalis 19 (1984), S. 330-334 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The constant mappings onto the unit form a zero subcategory of any category of monoid homomorphisms; a varietyV of monoids isalmost universal if every category of algebras is isomorphic to a class of all nonzero homomorphisms between members ofV. Almost universal monoid varieties are shown to be exactly those varieties containing all commutative monoids in which the identity xnyn=(xy)n fails for every n〉1. Almost universal varieties of monoids can also be characterized categorically as the varieties containing all groups with zero as one-object full subcategories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01201100
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  • 18
    Electronic Resource
    Electronic Resource
    Subdirectly dominated semigroup varieties (1997)
    Springer
    Algebra universalis 38 (1997), S. 15-35 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. A variety $ \Bbb V $ is subdirectly dominated if every algebra A in $ \Bbb V $ is embeddable into a subdirectly irreducible algebra belonging to $ \Bbb V $ . We characterize the subdirectly dominated semigroup varieties of nil semigroups, of commutative semigroups, and of completely regular semigroups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000120050036
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  • 19
    Electronic Resource
    Electronic Resource
    Endomorphisms and homomorphisms of Heyting algebras (1985)
    Springer
    Algebra universalis 20 (1985), S. 167-178 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a non-trivial Heyting algebraH, the cardinality of its endomorphism monoid is always at least two. If it is exactly two thenH is called 0-endomorphism rigid. It is shown that there exists a proper class of non-isomorphic 0-endomorphism rigid Heyting algebras. This is a consequence of a more general result: the variety of Heyting algebras is 0-universal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01278594
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  • 20
    Electronic Resource
    Electronic Resource
    Amalgamation in varieties of distributive double p-algebras (1994)
    Springer
    Algebra universalis 32 (1994), S. 407-438 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Distributive double p-algebras and regular double p-algebras are shown to have the amalgamation property (AP). Finitely generated varieties of distributive double p-algebras with the AP are characterized, and also varieties generated by algebras with a bounded finite number of maximal or minimal prime ideals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195722
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