Some results in the theory of linear non-associative algebras

Abstract

over if ra transformations, linearly independent or not, be arbitrarily assigned in dt to correspond to a basis of 21, then 8 is uniquely determined (and conversely) since 9Î determines 21 and 2Í, 2.An algebra 21 is here defined to be right-simple if and only if it contains no proper right ideals.Left-simplicity and simplicity are defined analogously.We do not exclude the case that 21 is the zero algebra of order one.Theorem 2A.2Í is right-simple, left-simple, or simple if and only if E(dt), E(%) or 7£(3i, £) respectively are irreducible algebras.Proof.The part of this theorem which deals with simplicity has been

Locations

• Transactions of the American Mathematical Society - View - PDF