TEST ELEMENTS AND RETRACTS OF FREE LIE-ALGEBRAS

Authors
MIKHALEV AA YU JT
Citation
Aa. Mikhalev et Jt. Yu, TEST ELEMENTS AND RETRACTS OF FREE LIE-ALGEBRAS, Communications in algebra, 25(10), 1997, pp. 3283-3289
Citations number
11
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Communications in algebra → ACNP
ISSN journal
00927872
Volume
25
Issue
10
Year of publication
1997
Pages
3283 - 3289
Database
ISI
SICI code
0092-7872(1997)25:10<3283:TEAROF>2.0.ZU;2-R
Abstract
An element u of a finitely generated flee Lie algebra L is a test elem ent if any endomorphism of L fixing u is an automorphism. We prove tha t test elements of L are precisely those elements not contained in any proper retract of L. In addition we characterize retracts of free Lie algebras.