Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero

1 Issue per year

CiteScore 2017: 0.28

SCImago Journal Rank (SJR) 2017: 0.231
Source Normalized Impact per Paper (SNIP) 2017: 0.443

Mathematical Citation Quotient (MCQ) 2017: 0.12

ICV 2017: 121.78

Open Access
See all formats and pricing
More options …
Volume 48, Issue 1


On the Directly and Subdirectly Irreducible Many-Sorted Algebras

J. Climent Vidal / J. Soliveres Tur
Published Online: 2015-03-11 | DOI: https://doi.org/10.1515/dema-2015-0001


A theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.

Keywords: many-sorted algebra; support of a many-sorted algebra; directly irreducible many-sorted algebra; subdirectly irreducible many-sorted algebra


  • [1] G. Birkhoff, Subdirect unions in universal algebra, Amer. Math. Soc. 50 (1944), 764-768.Google Scholar

  • [2] S. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer-Velag, 1981.CrossrefGoogle Scholar

  • [3] J. Climent, L. Fernandino, On the relation between many-sorted uniform 2-algebraic closure operators and many-sorted algebras, Collect. Math. 40 (1990), 93-101.Google Scholar

  • [4] J. Climent, J. Soliveres, On many-sorted algebraic closure operators, Math. Nachr. 266 (2004), 81-84.Google Scholar

  • [5] J. Climent, J. Soliveres, When is the insertion of the generators injective for a sur-reflective subcategory of a category of many-sorted algebras?, Houston J. Math. 35 (2009), 363-372. Google Scholar

About the article

Received: 2013-11-04

Revised: 2014-04-08

Published Online: 2015-03-11

Published in Print: 2015-03-01

Citation Information: Demonstratio Mathematica, Volume 48, Issue 1, Pages 1–12, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.1515/dema-2015-0001.

Export Citation

© by J. Climent Vidal. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Murat Bekar, Fouzi Hathout, and Yusuf Yayli
Asian-European Journal of Mathematics, 2017, Page 1850008

Comments (0)

Please log in or register to comment.
Log in