Interrelations between Annihilator, Dual and Pseudo-$H$-algebras
The annihilator operators play an important rôle in Wedderburn's type decompositions for pseudo-$H$-algebras. These operators determine the notions of annihilator, resp. dual topological algebras. Thus, it is quite natural to ask for possible relations between the latter topological algebras and those equipped with an $H$-structure. Among other things, we present necessary and sufficient conditions that a modular complemented $H$-algebra be annihilator. It is known that a dual algebra is annihilator, while the converse is not, in general, true. Our concern here is focused on appropriate conditions on a given $H$-algebra guaranteeing the coincidence of the notions dual and annihilator.
Annihilator algebra; Dual algebra;Semisimple algebra; Properly (resp. anti-properly) precomplemented $H$-algebra; (left, right) modular complemented $H$-algebra; Precomplemented $H$-algebra; Left (right) adjoint of an element; Pseudo
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eISSN 0975-8607; pISSN 0976-5905