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1
Content available remote Upper bounds on the sizes of finitely generated algebras
Berman J.
Demonstratio Mathematica
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2011
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Vol. 44, nr 3
447-471
EN
We present an upper bound for the cardinality of any n-generated algebra in a locally finite variety V of algebras. This upper bound depends only on some fundamental numerical invariants of the n-generated subdirectly irreducible algebras in V. A theorem characterizing those varieties that contain algebras whose cardinalities achieve the upper bound is proved. Several explicit methods for computing the exact values of these invariants are described. The final section contains detailed concrete examples illustrating applications of the characterization theorem and of the various methods for computing the upper bound.
2
Content available remote Representation of modals
Pilitowska A., Zamojska-Dzienio A.
Demonstratio Mathematica
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2011
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Vol. 44, nr 3
535-556
EN
The main aim of this paper is to describe the free objects in arbitrary varieties of modals (semilattice ordered idempotent and entropic algebras)and give some new representations of modals.
3
Content available remote Modes, modals, and barycentric algebras: a brief survey and an additivity theorem
Smith J. D. H.
Demonstratio Mathematica
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2011
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Vol. 44, nr 3
571-587
EN
Modes are idempotent and entropic algebras.Modals are both join semi lattices and modes,where the mode structure distributes over the join.Barycentric algebras are equipped with binary operations from the open unit interval,satisfying idempo tence,skew commutativity,and skew associativity.The article aims to give a brief survey of these structures and some of their applications.Special attention is devoted to hierar chical statistical mechanics and the modeling of complex systems.An additivity theorem for the entropy of independent combinations of systems is proved.
4
Content available remote Sameness between based universal algebras
Ricci G.
Demonstratio Mathematica
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2009
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Vol. 42, nr 1
3-22
EN
This is the continuation of the paper "Transformations between Menger systems". To define when two universal algebras with bases "are the same", here we propose a universal notion of transformation that comes from a triple characterization concerning three representation facets: the determinations of the Menger system, analytic monoid and endomorphism representation corresponding to a basis. Hence, this notion consists of three equivalent definitions. It characterizes another technical variant and also the universal version of the very semi-linear transformations that were coordinate-free. Universal transformations allow us to check the actual invariance of general algebraic constructions, contrary to the seeming invariance of representation-free thinking. They propose a new interpretation of free algebras as superpositions of "analytic spaces" and deny that our algebras differ from vector spaces at fundamental stages. Contrary to present beliefs, even the foundation of abstract Linear Algebra turns out to be incomplete.
5
Content available remote Pojęcia niezależności w ujęciu algebraicznym - ogólny schemat Marczewskiego
Głazek K.
Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
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1998
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[Z] 34
31-48
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