Graded pseudo-$H$-rings

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.