文摘
For a maximal separable subfield K of a central simple algebra A, we provide a semiring isomorphism between K–K-sub-bimodules of A and H–H A0;-sub-bisets of 85X&_mathId=si1.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=c4082f071a3b25df4d01375045348ab4" title="Click to view the MathML source">G=Gal(L/F), where 85X&_mathId=si2.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=8122aed7b306557ece5d8b044a5c5b15" title="Click to view the MathML source">F=Cent(A), L is the Galois closure of 85X&_mathId=si3.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=cbc8220786e49e3dcf935a6e9088e1e8" title="Click to view the MathML source">K/F, and 85X&_mathId=si4.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=e757791c6c1b0761ffdd4f4b4c60bdae" title="Click to view the MathML source">H=Gal(L/K). This leads to a combinatorial interpretation of the growth of 85X&_mathId=si5.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=ccbb0e680fdab58469922bd22ae11230" title="Click to view the MathML source">dimK((KaK)i), for fixed 85X&_mathId=si52.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=edb08b60ca88e1526634a648c51c0c04" title="Click to view the MathML source">a∈A, especially in terms of Kummer subspaces.