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arXiv · 2401.12897

Graded pseudo-H-rings

Antonio J. Calderón·Antonio Díaz·Marina Haralampidou·José M. Sánchez
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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.

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Antonio J. Calderón, Antonio Díaz, Marina Haralampidou, José M. Sánchez. 2024-01-23. Graded pseudo-H-rings. https://doi.org/10.15352/bjma%2F09-2-20

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