# The ordering of commutative terms

Czechoslovak Mathematical Journal (2006)

- Volume: 56, Issue: 1, page 133-154
- ISSN: 0011-4642

## Access Full Article

top## Abstract

top## How to cite

topJežek, Jaroslav. "The ordering of commutative terms." Czechoslovak Mathematical Journal 56.1 (2006): 133-154. <http://eudml.org/doc/31021>.

@article{Ježek2006,

abstract = {By a commutative term we mean an element of the free commutative groupoid $F$ of infinite rank. For two commutative terms $a$, $b$ write $a\le b$ if $b$ contains a subterm that is a substitution instance of $a$. With respect to this relation, $F$ is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered set has no automorphisms except the identity.},

author = {Ježek, Jaroslav},

journal = {Czechoslovak Mathematical Journal},

keywords = {definable; term; definability; term},

language = {eng},

number = {1},

pages = {133-154},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {The ordering of commutative terms},

url = {http://eudml.org/doc/31021},

volume = {56},

year = {2006},

}

TY - JOUR

AU - Ježek, Jaroslav

TI - The ordering of commutative terms

JO - Czechoslovak Mathematical Journal

PY - 2006

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 56

IS - 1

SP - 133

EP - 154

AB - By a commutative term we mean an element of the free commutative groupoid $F$ of infinite rank. For two commutative terms $a$, $b$ write $a\le b$ if $b$ contains a subterm that is a substitution instance of $a$. With respect to this relation, $F$ is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered set has no automorphisms except the identity.

LA - eng

KW - definable; term; definability; term

UR - http://eudml.org/doc/31021

ER -

## References

top- The lattice of equational theories. Part I: Modular elements, Czechoslovak Math. J. 31 (1981), 127–152. (1981) MR0604120
- The lattice of equational theories. Part II: The lattice of full sets of terms, Czechoslovak Math. J. 31 (1981), 573–603. (1981) MR0631604
- The lattice of equational theories. Part III: Definability and automorphisms, Czechoslovak Math. J. 32 (1982), 129–164. (1982) MR0646718
- The lattice of equational theories. Part IV: Equational theories of finite algebras, Czechoslovak Math. J. 36 (1986), 331–341. (1986) MR0831318
- Definability in the lattice of equational theories of semigroups, Semigroup Forum 46 (1993), 199–245. (1993) MR1200214
- 10.1090/S0002-9947-03-03351-8, Trans. Amer. Math. Soc. 356 (2004), 3483–3504. (2004) Zbl1050.08005MR2055743DOI10.1090/S0002-9947-03-03351-8
- Algebras, Lattices, Varieties, Volume I, Wadsworth & Brooks/Cole, Monterey, CA, 1987. (1987) MR0883644

## Citations in EuDML Documents

top## NotesEmbed ?

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