On reductive and distributive algebras

Anna B. Romanowska

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 4, page 617-629
  • ISSN: 0010-2628

Abstract

top
The paper investigates idempotent, reductive, and distributive groupoids, and more generally Ω -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left k -step reductive Ω -algebras, and of right n -step reductive Ω -algebras, are independent for any positive integers k and n . This gives a structural description of algebras in the join of these two varieties.

How to cite

top

Romanowska, Anna B.. "On reductive and distributive algebras." Commentationes Mathematicae Universitatis Carolinae 40.4 (1999): 617-629. <http://eudml.org/doc/248406>.

@article{Romanowska1999,
abstract = {The paper investigates idempotent, reductive, and distributive groupoids, and more generally $\Omega $-algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left $k$-step reductive $\Omega $-algebras, and of right $n$-step reductive $\Omega $-algebras, are independent for any positive integers $k$ and $n$. This gives a structural description of algebras in the join of these two varieties.},
author = {Romanowska, Anna B.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {idempotent and distributive groupoids and algebras; Mal'cev products of varieties of algebras; independent varieties; idempotent and distributive algebra; Mal'tsev products of varieties of algebras; independent varieties of algebras},
language = {eng},
number = {4},
pages = {617-629},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On reductive and distributive algebras},
url = {http://eudml.org/doc/248406},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Romanowska, Anna B.
TI - On reductive and distributive algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 4
SP - 617
EP - 629
AB - The paper investigates idempotent, reductive, and distributive groupoids, and more generally $\Omega $-algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left $k$-step reductive $\Omega $-algebras, and of right $n$-step reductive $\Omega $-algebras, are independent for any positive integers $k$ and $n$. This gives a structural description of algebras in the join of these two varieties.
LA - eng
KW - idempotent and distributive groupoids and algebras; Mal'cev products of varieties of algebras; independent varieties; idempotent and distributive algebra; Mal'tsev products of varieties of algebras; independent varieties of algebras
UR - http://eudml.org/doc/248406
ER -

References

top
  1. Dehornoy P., Notes on Self-distributivity, preprint, Mathématiques, Université de Caen, France. 
  2. Dudek J., On varieties of groupoid modes, Demonstratio Math. 27 (1994), 815-828. (1994) Zbl0835.08003MR1319426
  3. Grätzer G., Lakser H., Płonka J., Joins and direct product of equational classes, Canad. Math. Bull. 12 (1969), 741-744. (1969) MR0276160
  4. Ježek J., Kepka T., Němec P., Distributive Groupoids, Academia Praha (1981). (1981) MR0672563
  5. Knoebel A., A product of independent algebras with finitely generated identities, Algebra Universalis 3 (1973), 147-151. (1973) MR0349543
  6. Mal'cev A.I., Multiplication of classes of algebraic systems (in Russian), Sibirsk. Mat. Zh. 8 (1967), 346-365. (1967) MR0213276
  7. Pilitowska A., Romanowska A., Reductive modes, Periodica Math. Hung. 36 (1998), 67-78. (1998) Zbl0924.08001MR1684506
  8. Płonka J., Romanowska A., Semilattice sums, Universal Algebra and Quasigroups (eds. A. Romanowska, J.D.H. Smith), Heldermann Verlag, Berlin (1992), 123-158. (1992) MR1191231
  9. Pilitowska A., Romanowska A., Roszkowska B., Products of mode varieties and algebras of subalgebras, Math. Slovaca 46 (1996), 497-514. (1996) Zbl0890.08003MR1451038
  10. Romanowska A., Smith J.D.H., Modal Theory, Heldermann Verlag, Berlin, 1985. Zbl0553.08001MR0788695
  11. Romanowska A., Traina S., Algebraic quasi-orders and sums of algebras, Discuss. Math. Algebra Stochastic Methods 19 (1999), 239-263. (1999) Zbl0949.08001MR1709970

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.