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Fri, 10 Nov 2017 14:43:42 +0100Fri, 10 Nov 2017 14:43:42 +0100Order-semi-primal lattices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5073
Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5073Fri, 10 Nov 2017 14:43:42 +0100Representations by order-polynomially complete lattices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5072
Bernd Kilgus; Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5072Fri, 10 Nov 2017 14:38:25 +0100Strictly order primal algebras
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5071
Otfried Lüders; Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5071Fri, 10 Nov 2017 14:33:13 +0100Pre-fixed points of polynomial functions in lattices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5070
Marcel Erne; Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5070Fri, 10 Nov 2017 14:25:34 +0100Polynomial functions of modular lattices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5060
A polynomial function \(f : L \to L\) of a lattice \(\mathcal{L}\) = \((L; \land, \lor)\) is generated by the identity function id \(id(x)=x\) and the constant functions \(c_a (x) = a\) (for every \(x \in L\)), \(a \in L\) by applying the operations \(\land, \lor\) finitely often. Every polynomial function in one or also in several variables is a monotone function of \(\mathcal{L}\).
If every monotone function of \(\mathcal{L}\)is a polynomial function then \(\mathcal{L}\) is called orderpolynomially complete. In this paper we give a new characterization of finite order-polynomially lattices. We consider doubly irreducible monotone functions and point out their relation to tolerances, especially to central relations. We introduce chain-compatible lattices
and show that they have a non-trivial congruence if they contain a finite interval and an infinite chain. The consequences are two new results. A modular lattice \(\mathcal{L}\) with a finite interval is order-polynomially complete if and only if \(\mathcal{L}\) is finite projective geometry. If \(\mathcal{L}\) is simple modular lattice of infinite length then every nontrivial interval is of infinite length and has the same cardinality as any other nontrivial interval of \(\mathcal{L}\). In the last sections we show the descriptive power of polynomial functions of
lattices and present several applications in geometry.Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5060Fri, 10 Nov 2017 09:47:24 +0100On derived varieties
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5059
Derived varieties play an essential role in the theory of hyperidentities. In [11] we have shown that derivation diagrams are a useful tool in the analysis of derived algebras and varieties. In this paper this tool is developed further in order to use it for algebraic constructions of derived algebras. Especially the operator \(S\) of subalgebras, \(H\) of homomorphic irnages and \(P\) of direct products are studied. Derived groupoids from the groupoid \(N or (x,y)\) = \(x'\wedge y'\) and from abelian groups are considered. The latter class serves as an example for fluid algebras and varieties. A fluid variety \(V\) has no derived variety as a subvariety and is introduced as a counterpart for solid varieties. Finally we use a property of the commutator of derived algebras in order to show that solvability and nilpotency are preserved under derivation.Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5059Fri, 10 Nov 2017 09:22:23 +0100Hyperidentities
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5024
The concept of a free algebra plays an essential role in universal algebra and in computer science. Manipulation of terms, calculations and the derivation of identities are performed in free algebras. Word problems, normal forms, system of reductions, unification and finite bases of identities are topics in algebra and logic as well as in computer science. A very fruitful point of view is to consider structural properties of free algebras. A.I. Malcev initiated a thorough research of the congruences of free algebras. Henceforth congruence permutable, congruence distributive and congruence modular varieties are
intensively studied. A lot of Malcev type theorems are connected to the congruence lattice of free algebras. Here we consider free algebras as semigroups of compositions of terms and more specific as clones of terms. The properties of these semigroups and clones are adequately described by hyperidentities. Naturally a lot of theorems of "semigroup" or "clone" type can be derived. This topic of research is still in its beginning and therefore a lot öf concepts and results cannot be presented in a final and polished form. Furthermore a lot of problems and questions are open which are of importance for the further development of the theory of hyperidentities.Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5024Fri, 03 Nov 2017 10:10:27 +0100Derived Varieties of Semigroups and Groupoids
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4889
Dietmar Schweigert; S.L. Wismathreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4889Thu, 19 Oct 2017 11:35:28 +0200Diskrete Mathematik
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1658
Vorlesungsskript Diskrete MathematikDietmar Schweigertlecturehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1658Thu, 01 Sep 2005 15:32:02 +0200Universal Algebra
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1493
Handwritten digitized script to Prof. Schweigert's lecture "Universal Algebra"Dietmar Schweigertlecturehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1493Thu, 05 Feb 2004 13:38:39 +0100Hyperquasivarieties
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1424
We consider the notion of hyper-quasi-identities and hyperquasivarieties, as a common generalization of the concept of quasi-identity and quasivariety invented by A.I. Mal'cev, cf. [10], cf. [5] and hypervariety invented by the authors in [6].Ewa Graczynska; Dietmar Schweigertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1424Sat, 30 Aug 2003 17:30:49 +0200Logic
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1265
Handwritten digitized script to Prof. Schweigert's lecture "Logic"Dietmar Schweigertlecturehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1265Tue, 27 Nov 2001 00:00:00 +0100Presentation of power-ordered sets
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1259
Power-ordered sets are not always lattices. In the case of distributive lattices we give a description by disjoint of chains. Finite power-ordered sets have a polarity. We introduct the leveled lattices and show examples with trivial tolerance. Finally we give a list of Hasse diagrams of power-ordered sets.Dietmar Schweigertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1259Fri, 07 Sep 2001 00:00:00 +0200Graphentheoretische Methoden der Optimierung
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1056
Dietmar Schweigertlecturehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1056Mon, 10 Jul 2000 00:00:00 +0200A reduction algorithm for integer multiple objective linear programs
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/483
We consider a multiple objective linear program (MOLP) max{Cx|Ax = b,x in N_{0}^{n}} where C = (c_ij) is the p x n - matrix of p different objective functions z_i(x) = c_{i1}x_1 + ... + c_{in}x_n , i = 1,...,p and A is the m x n - matrix of a system of m linear equations a_{k1}x_1 + ... + a_{kn}x_n = b_k , k=1,...,m which form the set of constraints of the problem. All coefficients are assumed to be natural numbers or zero. The set M of admissable solutions {hat x} is an admissible solution such that there exists no other admissable solution x' with C{hat x} Cx'. The efficient solutions play the role of optimal solutions for the MOLP and it is our aim to determine the set of all efficient solutionsDietmar Schweigert; Peter Neumayerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/483Mon, 03 Apr 2000 00:00:00 +0200Minimal paths on ordered graphs
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/497
To present the decision maker's (DM) preferences in multicriteria decision problems as a partially ordered set is an effective method to catch the DM's purpose and avoid misleading results. Since our paper is focused on minimal path problems, we regard the ordered set of edges (E,=). Minimal paths are defined in repect to power-ordered sets which provides an essential tool to solve such problems. An algorithm to detect minimal paths on a multicriteria minimal path problem is presentedUlrike Bossong; Dietmar Schweigertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/497Mon, 03 Apr 2000 00:00:00 +0200Clones preserving a quasi-order
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/830
It is proved that if a finite non-trivial quasi-order is nota linear order then there exist continuum many clones, whichconsist of functions preserving the quasi-order and containall unary functions with this property. It is shown that, fora linear order on a three-element set, there are only 7 suchclonesAndrei A. Krokhin; Dietmar Schweigertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/830Mon, 03 Apr 2000 00:00:00 +0200Vorlesung Logik
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1049
Dietmar Schweigertlecturehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1049Fri, 10 Mar 2000 00:00:00 +0100Locally Maximal Clones II
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/842
Ivo Rosenberg; Dietmar Schweigertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/842Mon, 07 Feb 2000 00:00:00 +0100