Namespaces
Variants
Actions

Difference between revisions of "Magari theorem"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(→‎References: expand bibliodata)
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
The assertion that every [[Variety of universal algebras|variety of universal algebras]] with a non-trivial member contains also a member whose lattice of congruences is <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m110/m110030/m1100301.png" />-element. Such universal algebras are called congruence-simple or simple [[#References|[a1]]] (see also [[Universal algebra|Universal algebra]]).
+
{{TEX|done}}
 +
The assertion that every [[Variety of universal algebras|variety of universal algebras]] with a non-trivial member contains also a member whose lattice of congruences is $2$-element. Such universal algebras are called congruence-simple or simple [[#References|[a1]]] (see also [[Universal algebra|Universal algebra]]).
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  S. Burris,  H.P. Sankappanavar,  "A course in universal algebra" , Springer  (1981)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  R. Magari,  "Una dimonstrazione del fatto che ogni varietà ammette algebre semplici"  ''Ann. Univ. Ferrara Sez. VII (N.S.)'' , '''14'''  (1969)  pp. 1–4</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  B. Csákány,  "Magari via Malcev"  ''Algebra Universalis'' , '''36'''  (1996)  pp. 421–422</TD></TR></table>
+
<table>
 +
<TR><TD valign="top">[a1]</TD> <TD valign="top">  S. Burris,  H.P. Sankappanavar,  "A course in universal algebra" , Springer  (1981) {{ZBL|0478.08001}}</TD></TR>
 +
<TR><TD valign="top">[a2]</TD> <TD valign="top">  R. Magari,  "Una dimonstrazione del fatto che ogni varietà ammette algebre semplici"  ''Ann. Univ. Ferrara Sez. VII (N.S.)'' , '''14'''  (1969)  pp. 1–4 {{DOI|10.1007/BF02896794}}  {{ZBL|0247.08016}}</TD></TR>
 +
<TR><TD valign="top">[a3]</TD> <TD valign="top">  B. Csákány,  "Magari via Malcev"  ''Algebra Universalis'' , '''36'''  (1996)  pp. 421–422 {{DOI|10.1007/BF01236767}} {{ZBL|0901.08008}}</TD></TR>
 +
</table>

Latest revision as of 17:48, 24 March 2018

The assertion that every variety of universal algebras with a non-trivial member contains also a member whose lattice of congruences is $2$-element. Such universal algebras are called congruence-simple or simple [a1] (see also Universal algebra).

References

[a1] S. Burris, H.P. Sankappanavar, "A course in universal algebra" , Springer (1981) Zbl 0478.08001
[a2] R. Magari, "Una dimonstrazione del fatto che ogni varietà ammette algebre semplici" Ann. Univ. Ferrara Sez. VII (N.S.) , 14 (1969) pp. 1–4 DOI 10.1007/BF02896794 Zbl 0247.08016
[a3] B. Csákány, "Magari via Malcev" Algebra Universalis , 36 (1996) pp. 421–422 DOI 10.1007/BF01236767 Zbl 0901.08008
How to Cite This Entry:
Magari theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Magari_theorem&oldid=12266
This article was adapted from an original article by A. Muravitsky (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article