Banach Journal of Mathematical Analysis

Graded pseudo-$H$-rings

José María Sánchez Delgado, Antonio Jesús Calderón Martín, Antonio Díaz Ramos, and Marina Haralampidou

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Abstract

Consider a pseudo-$H$-space $E$ endowed with a separately continuous biadditive associative multiplication which induces a grading on $E$ with respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring and we show that it has the form $E = cl(U + \sum_j I_j)$ with $U$ a closed subspace of $E_1$ (the summand associated to the unit element in $G$), and any $I_j$ runs over a well described closed graded ideal of $E$, satisfying $I_jI_k = 0$ if $j \neq k$. We also give a context in which graded simplicity of $E$ is characterized. Moreover, the second Wedderburn-type theorem is given for certain graded pseudo-$H$-rings.

Article information

Source
Banach J. Math. Anal., Volume 9, Number 2 (2015), 311-321.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1419001119

Digital Object Identifier
doi:10.15352/bjma/09-2-20

Mathematical Reviews number (MathSciNet)
MR3296120

Zentralblatt MATH identifier
1314.13002

Subjects
Primary: 46H10: Ideals and subalgebras
Secondary: 46H20: Structure, classification of topological algebras 13A02: Graded rings [See also 16W50] 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Keywords
Topological ring pseudo-$H$-ring graded pseudo-$H$-ring graded ideal graded simple

Citation

Calderón Martín, Antonio Jesús; Díaz Ramos, Antonio; Haralampidou, Marina; Sánchez Delgado, José María. Graded pseudo-$H$-rings. Banach J. Math. Anal. 9 (2015), no. 2, 311--321. doi:10.15352/bjma/09-2-20. https://projecteuclid.org/euclid.bjma/1419001119


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