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2015 Graded pseudo-$H$-rings
José María Sánchez Delgado, Antonio Jesús Calderón Martín, Antonio Díaz Ramos, Marina Haralampidou
Banach J. Math. Anal. 9(2): 311-321 (2015). DOI: 10.15352/bjma/09-2-20

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.

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José María Sánchez Delgado. Antonio Jesús Calderón Martín. Antonio Díaz Ramos. Marina Haralampidou. "Graded pseudo-$H$-rings." Banach J. Math. Anal. 9 (2) 311 - 321, 2015. https://doi.org/10.15352/bjma/09-2-20

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1314.13002
MathSciNet: MR3296120
Digital Object Identifier: 10.15352/bjma/09-2-20

Subjects:
Primary: 46H10
Secondary: 13A02, 46C05, 46H20

Rights: Copyright © 2015 Tusi Mathematical Research Group

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