Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1156.20048
Cain, Alan J.; Robertson, Edmund F.; Ruškuc, Nik
Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions. (English)
[J] J. Aust. Math. Soc. 84, No. 1, 39-61 (2008). ISSN 1446-7887; ISSN 1446-8107

It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index [see {\it C. M. Campbell}, {\it E. F. Robertson}, {\it N. Ruškuc} and {\it R. M. Thomas}, Semigroup Forum 51, No. 1, 47-62 (1995; Zbl 0833.20069); {\it N. Ruškuc}, Proc. Lond. Math. Soc., III. Ser. 76, No. 2, 383-405 (1998; Zbl 0891.20036)]. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative, right-cancellative presentations. Let $S$ be a semigroup that embeds into a group. Let $T$ be a subsemigroup of $S$ of finite Rees index. Then $S$ has finite Malcev presentation if and only if $T$ has a finite Malcev presentation.
[Aleksandr V. Tishchenko (Moskva)]

MSC 2000:: *20M05 Free semigroups

Keywords: Malcev presentations; cancellative presentations; finitely presented semigroups; subsemigroups of finite index; rewriting systems; group-embeddable semigroups

Citations: Zbl 0833.20069; Zbl 0891.20036

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.
	Elementary number theory. Primes, congruences, and secrets.

Simple Search

Zentralblatt MATH Berlin [Germany]