Our work goes in two directions. At first we want to transfer definitions,
concepts and results of the theory of hyperidentities and solid varieties from
the total to the partial case.
(1) We prove that the operators chi^A_RNF and chi^E_RNF are only monotone and
additive and we show that the sets of all fixed points of these operators are
characterized only by three instead of four equivalent conditions for the case
of closure operators.
(2) We prove that V is n − SF-solid iff clone^SF V is free with respect to
itself, freely generated by the independent set {[fi(x_1, . . . / x_n)]Id^SF_n V | i in I}.
(3) We prove that if V is n-fluid and ~V |P(V ) =~V −iso |P(V ) then V is kunsolid
for k >= n (where P(V ) is the set of all V -proper hypersubstitutions of type tau ).
(4) We prove that a strong M-hyperquasi-equational theory is characterized
by four equivalent conditions.
The second direction of our work is to follow ideas which are typical for the
partial case.
(1) We characterize all minimal partial clones which are strongly solidifyable.
(2)We define the operator Chi^A_Ph where Ph is a monoid of regular partial hypersubstitutions.Using this concept, we define the concept of a Phyp_R(tau )-solid strong regular variety of partial algebras and we prove that a PHyp_R(tau )-solid strong regular variety satisfies four equivalent conditions.
| Identifer | oai:union.ndltd.org:Potsdam/oai:kobv.de-opus-ubp:1204 |
| Date | January 2006 |
| Creators | Busaman, Saofee |
| Publisher | Universität Potsdam, Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik |
| Source Sets | Potsdam University |
| Language | English |
| Detected Language | English |
| Type | Text.Thesis.Doctoral |
| Format | application/pdf |
| Rights | http://opus.kobv.de/ubp/doku/urheberrecht.php |
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