Distributive differential modals

Karolina Ślusarska

Discussiones Mathematicae - General Algebra and Applications (2008)

  • Volume: 28, Issue: 1, page 29-47
  • ISSN: 1509-9415

Abstract

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A differential modal is an algebra with two binary operations such that one of the reducts is a differential groupoid and the other is a semilattice, and with the groupoid operation distributing over the semilattice operation. The aim of this paper is to show that the varieties of entropic and distributive differential modals coincide, and to describe the lattice of varieties of entropic differential modals.

How to cite

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Karolina Ślusarska. "Distributive differential modals." Discussiones Mathematicae - General Algebra and Applications 28.1 (2008): 29-47. <http://eudml.org/doc/276857>.

@article{KarolinaŚlusarska2008,
abstract = {A differential modal is an algebra with two binary operations such that one of the reducts is a differential groupoid and the other is a semilattice, and with the groupoid operation distributing over the semilattice operation. The aim of this paper is to show that the varieties of entropic and distributive differential modals coincide, and to describe the lattice of varieties of entropic differential modals.},
author = {Karolina Ślusarska},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {differential groupoid; mode; modal; free differential modal},
language = {eng},
number = {1},
pages = {29-47},
title = {Distributive differential modals},
url = {http://eudml.org/doc/276857},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Karolina Ślusarska
TI - Distributive differential modals
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 1
SP - 29
EP - 47
AB - A differential modal is an algebra with two binary operations such that one of the reducts is a differential groupoid and the other is a semilattice, and with the groupoid operation distributing over the semilattice operation. The aim of this paper is to show that the varieties of entropic and distributive differential modals coincide, and to describe the lattice of varieties of entropic differential modals.
LA - eng
KW - differential groupoid; mode; modal; free differential modal
UR - http://eudml.org/doc/276857
ER -

References

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  1. [1] K.A. Kearnes, Semilattice modes I: the associated semiring, Algebra Universalis 34 (1995), 220-272. Zbl0848.08005
  2. [2] A. Romanowska, On some representations of groupoid modes satisfying the reduction law, Demonstratio Mathematica 21 (1988), 943-960. Zbl0677.20057
  3. [3] A. Romanowska and B. Roszkowska, On some groupoid modes, Demonstratio Mathematica 20 (1987), 277-290. Zbl0669.08005
  4. [4] A. Romanowska and B. Roszkowska, Representations of n-cyclic groupoids, Algebra Universalis 26 (1989), 7-15. Zbl0669.20058
  5. [5] A.B. Romanowska and J.D.H. Smith, Modes, World Scientific, Singapore 2002. 
  6. [6] A.B. Romanowska and J.D.H. Smith, Modal Theory - an Algebraic Approach to Order, Geometry and Convexity, Heldermann Verlag, Berlin 1985. Zbl0553.08001
  7. [7] A.B. Romanowska and J.D.H. Smith, Differential groupoids, Contribution to General Algebra 7 (1991), 283-290. Zbl0744.20055

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