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  • 1
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    Ideals and congruence kernels of algebras (1996)
    Springer
    Details
    Publication Date: 1996-01-01
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
    Published by Springer
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    PAPER CURRENT
  • 2
    Electronic Resource
    Electronic Resource
    Some maximal closed classes of operations on infinite sets (1974)
    Springer
    Mathematische Annalen 212 (1974), S. 157-164 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01350783
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On generating large classes of Sheffer functions (1978)
    Springer
    Aequationes mathematicae 17 (1978), S. 164-181 
    Details
    ISSN: 1420-8903
    Keywords: Primary 08A25 ; Secondary 02C05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let A be a finite set,n 〉 1 andD $$ \subseteq $$ A n . We say thatf:D → A is a partial Sheffer function of size |D| if eachf*: A n → A agreeing withf onD is Sheffer (or complete that is 〈A; f〉 primal), i.e. iff* generates allg:A m → A (m = 1, 2, ⋯) via repeated composition. The least size of a partial Sheffer function is shown to be |A| + 2 and all partial Sheffer functions of this size are exhibited. This shows how surprisingly little information onf is needed to ensure thatf is Sheffer and, at the same time, gives a description of large classes of Sheffer functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01818558
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  • 4
    Electronic Resource
    Electronic Resource
    A projection property (1996)
    Springer
    Algebra universalis 36 (1996), S. 159-184 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract E. Corominas introduced recently this notion for posets:P is projective if every mapf fromP 2 toP which is order preserving and idempotent (i.e.f(x, x)=x for allx ε P) is a projection. We consider extensions of this notion to other structures, as well as to maps withn variables. We prove thatn-projectivity forn≥2 is equivalent to 2-projectivity, with a single exception: the structure has the same morphisms as the collection of congruences associated with a vector space over ℤ/2, of dimension at least two. Focusing on relational structures, Arrow's Theorem is introduced as an example. We consider particular types of relational structures: posets, graphs and metric spaces, and discuss for these the specific examples of crowns, cycles and circles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01234102
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  • 5
    Electronic Resource
    Electronic Resource
    Ideals and the binary discriminator in universal algebra (1999)
    Springer
    Algebra universalis 42 (1999), S. 239-251 
    Details
    ISSN: 1420-8911
    Keywords: Key words: Algebra with 0, variety with 0, ideal, ternary and binary discriminator and dual discriminator, 0-primal algebras, binary discriminator and binary dual discriminator varieties.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We introduce the binary discriminator and the dual binary discriminator and the corresponding universal algebras with 0. The latter are related to permutability and distributivity at 0. For A finite the dual binary discriminator is in the intersection of all maximal subclones of the clone of all f satisfying f (0,...,0) = 0 (except certain maximal subclones if A is of prime power cardinality). An algebra with a special binary term function and a special unary term function is a dual binary discriminator algebra if and only if it is ideal-free. Finally we characterize binary and dual binary discriminator varieties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000120050001
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  • 6
    Electronic Resource
    Electronic Resource
    The set of maximal closed classes of operations on an infinite setA has cardinality $$2^{2^{^{\left| A \right|} } }$$ (1976)
    Springer
    Archiv der Mathematik 27 (1976), S. 561-568 
    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/BF01224718
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  • 7
    Electronic Resource
    Electronic Resource
    On generating large classes of Sheffer functions (1977)
    Springer
    Aequationes mathematicae 16 (1977), S. 316-318 
    Details
    ISSN: 1420-8903
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01836051
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  • 8
    Electronic Resource
    Electronic Resource
    Large classes of functionally complete groupoids I (1982)
    Springer
    Aequationes mathematicae 25 (1982), S. 274-288 
    Details
    ISSN: 1420-8903
    Keywords: Primary 08A25, 02C05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetA be a finite set,n≥1 andD⊆A n. We say thatf :D →A is a functionally complete partial operation of size |D| if eachf*:A n →A agreeing withf onD is functionally complete. Such an operation of sized represents thus a family of $$|A|^{(|A|^n - d)} $$ functionally complete operations. We investigate the least possible size of functionally complete partial groupoids. Such groupoids not defined on a row or column have size either |A|+1 or |A|+2 or are of size at least 2|A|−2. We prove that |A|+1 is the least size of such a groupoid and completely determine those of size |A|+1. As one might expect, these groupoids are very special. This study shows how surprisingly little information is needed to ensure that a groupoid is functionally complete and, at the same time, gives a description of large classes of functionally complete groupoids.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02189623
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  • 9
    Electronic Resource
    Electronic Resource
    Local completeness I (1984)
    Springer
    Algebra universalis 18 (1984), S. 308-326 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An infinite algebra is locally complete if its local closure is the set of all finitary operations. We give a local completeness criterion in terms of a system R of finitary relations on A such that the polymorph Pol ρ of each ρ εR is locally incomplete and for every locally incomplete algebra 〈A; F〉 we have F ⊑ Pol ρ for some ρ ε R. This system consists of (i) certain natural relations whose polymorphs are best possible in the sense that they are co-atoms in the lattice of locally closed incomplete algebras, (ii) five types of binary relations, (iii) one type of ternary relations and (iv) at least ternary totally reflexive and symmetric relations that are not locally central.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01203368
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  • 10
    Electronic Resource
    Electronic Resource
    Completeness theory for finite partial algebras (1992)
    Springer
    Algebra universalis 29 (1992), S. 378-401 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetA be a finite universe of cardinality ¦A¦ 〉- 3. We characterize the non quasi-diagonai strongly reflexive relations that determine maximal partial clones onA. Combining this with some known results, we deduce a general completeness criterion for finite partial algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212439
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