Embedding nil algebras in train algebras

Abstract

We generalize the classical example, due to Abraham, of a train algebra that is not special train, to non necessarily commutative right nil algebras of index n.

Power-associative algebras that are train algebras

“…(ii) Recall from [9] that if (A, ω) is a baric algebra with idempotent e such that ker(ω) is nil of nil-index d 2, and if there is λ ∈ K with ea = λa for all a ∈ ker(ω), then (A, ω) is a train algebra of train polynomial X d+1 + γ 1 X d + · · · + γ d X , where…”

E-Ideals in baric algebras: basic properties

“…For the proof of the next proposition, we need to introduce some notation and quote a result from [6]. Let A be an arbitrary algebra over F and let f t : A -> K i3 where The solution of this system shows that each c, e E A (p) and so also c n = b" = p(fc) G E A (p) and this proves the proposition.…”

“…Let £ be a field and (A, w) a commutative baric algebra over For a given representation of / in the form (6), we consider the integer max{; : y tJ ^ 0} and define the degree of/ as the minimum of these numbers, when we allow all possible representations of / in the form (6). The corresponding representation will be referred to as the minimal representation of/.…”

Algebraic structure of genetic inheritance

“…A random sampling of current references might include Wörz-Busekros [37]; Walcher [33]; Guzzo [18], [19]; Costa and Guzzo [7], [8]; Hentzel, Peresi, and Holgate [21]; Peresi [31]; Cortés [6]; Martinez [28]; Burgueño, Neuberg, and Suazo [5]; González and Martinez [16]; and González, Martinez, and Vicente [17]. This list is by no means complete, but it does provide a starting point for some of the current work being done in the field.…”