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We are interested in the evolution operators defined on commutative and non-associative algebras when the characteristic of the scalar field is 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic, and plenary train operators. They are studied and classified for non-baric and for baric algebras. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study plenary train algebras of arbitrary rank. We show that for most parameter choices of the train identity, the additional identity is satisfied. We also find sufficient conditions for A to have idempotents. [Copyright &y& Elsevier]

We study train algebras of fourth degree, give some genetic examples and explicit the plenary train identities associated. These algebras fall ultimately into four classes; the first two of them do not have 1/2 as train root and thus have idempotents. For these types we provide structure theorems, which are then used for classification purposes in small dimensions. [ABSTRACT FROM AUTHOR]