G. Lakshmi | Sri Krishnadevaraya University (original) (raw)
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Leibnitz-derivation of 0-torsion finite dimensional flexible algebras over an algebraically close... more Leibnitz-derivation of 0-torsion finite dimensional flexible algebras over an algebraically closed field is described. This class of algebra with unit element 1 is nilpotent if and only if it admits an invertible Leibnitz-derivation. This is an analogue to Moens theorem. The proofs are elementary in nature and based on the techniques adopted by Myung and Elduque.
Background: First examples of simple nonassociative superalgebras were constructed by Shestakov i... more Background: First examples of simple nonassociative superalgebras were constructed by Shestakov in (1991 and 1992). Since then many authors showed interest towards the study of superalgebras and superalgebras of vector type.
Materials and Methods: Multiplication in M is uniquely defined by a fixed finite set of derivations and by elements of A. The types of derivations used in this article to obtain the results are the near derivation , the derivation and the derivation
Results: The flexible Lie - admissible superalgebra over a 2, 3 – torsion free field on one odd generator e is isomorphic to the twisted superalgebra with the free generator In a 2, 3 – torsion free flexible Lie - admissible superalgebras of vector type F, the even part A is differentiably simple, associative and commutative algebra and the odd part M is a finitely generated associative and commutative A – bimodule.
Conclusions: A connection between the integral domains, the finitely generated projective modules over them, the derivations of an integral domain and the flexible Lie – admissible superalgebras of vector type has been established.
Main conclusions: If A is an integral domain and be a finitely generated projective A-module of rank 1, then is a flexible Lie - admissible superalgebra with even part A and odd part M provided that the mapping is a nonzero derivation of A into the A - module , is a set of derivations of A where .
Leibnitz-derivation of 0-torsion finite dimensional flexible algebras over an algebraically close... more Leibnitz-derivation of 0-torsion finite dimensional flexible algebras over an algebraically closed field is described. This class of algebra with unit element 1 is nilpotent if and only if it admits an invertible Leibnitz-derivation. This is an analogue to Moens theorem. The proofs are elementary in nature and based on the techniques adopted by Myung and Elduque.
Background: First examples of simple nonassociative superalgebras were constructed by Shestakov i... more Background: First examples of simple nonassociative superalgebras were constructed by Shestakov in (1991 and 1992). Since then many authors showed interest towards the study of superalgebras and superalgebras of vector type.
Materials and Methods: Multiplication in M is uniquely defined by a fixed finite set of derivations and by elements of A. The types of derivations used in this article to obtain the results are the near derivation , the derivation and the derivation
Results: The flexible Lie - admissible superalgebra over a 2, 3 – torsion free field on one odd generator e is isomorphic to the twisted superalgebra with the free generator In a 2, 3 – torsion free flexible Lie - admissible superalgebras of vector type F, the even part A is differentiably simple, associative and commutative algebra and the odd part M is a finitely generated associative and commutative A – bimodule.
Conclusions: A connection between the integral domains, the finitely generated projective modules over them, the derivations of an integral domain and the flexible Lie – admissible superalgebras of vector type has been established.
Main conclusions: If A is an integral domain and be a finitely generated projective A-module of rank 1, then is a flexible Lie - admissible superalgebra with even part A and odd part M provided that the mapping is a nonzero derivation of A into the A - module , is a set of derivations of A where .