Unions of Parafree Lie Algebras

Abstract

We consider unions of parafree Lie algebras and we prove that such unions are again parafree under some conditions.

On Parafree Leibniz Algebras

“…H. Baur [4] defined a non-free parafree Lie algebra. Further, N. Ekici and Z. Velioğlu have worked on some important results of parafree Lie algebras [6,7] and Z. Velioğlu has investigated the subalgebras and quotient algebras of parafree Lie algebras [11]. In this paper following [2] we focus on parafree Leibniz algebras and state all important known results for such algebras.…”

Parafree Center-by-Metabelian Lie Algebras

“…He obtained basic results which provide a solid understanding of the structure of parafree Lie algebras. In [9], N. Ekici and Z. Velioglu considered unions of parafree Lie algebras and they prove that such unions are again parafree under some conditions. In [10], N. Ekici and Z. Velioglu proved that the direct limit of any directed system of parafree Lie algebras exists in the variety of parafree Lie algebras.…”

“…In [9], N. Ekici and Z. Velioglu considered unions of parafree Lie algebras and they prove that such unions are again parafree under some conditions. In [10], N. Ekici and Z. Velioglu proved that the direct limit of any directed system of parafree Lie algebras exists in the variety of parafree Lie algebras. Baumslag's and Baur's works have given a start for studies in the theory of parafree Lie algebras.…”

Paraserbest Lie Cebirlerinin Ters Limiti

“…Baur paraserbest grupların tanımını Lie cebirlerine uyarlayarak paraserbest Lie cebirlerinin tanımını yapmıştır [5]. Daha sonra Ekici ve Velioğlu paraserbest Lie cebirlerinin direkt limiti [6] ve birleşimi [7] üzerinde çalışmalar yapmıştır.…”