Interrelations between Annihilator, Dual and Pseudo-$H$-algebras

Authors

  • Marina Haralampidou Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece (Hellas)

DOI:

https://doi.org/10.26713/cma.v3i1.142

Keywords:

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

Abstract

The annihilator operators play an important rí´le 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.

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CITATION

How to Cite

Haralampidou, M. (2012). Interrelations between Annihilator, Dual and Pseudo-$H$-algebras. Communications in Mathematics and Applications, 3(1), 25–38. https://doi.org/10.26713/cma.v3i1.142

Issue

Vol. 3 No. 1 (2012)

Section

Research Article

License

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