Bimodule structure of central simple algebras

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• 作者：Eliyahu Matzri^a ; ^{elimatzri@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Louis H. Rowen^a ; ^{rowen@math.biu.ac.il" class="auth_mail" title="E-mail the corresponding author} ; David Saltman^b ; ^{saltman@idaccr.org" class="auth_mail" title="E-mail the corresponding author} ; Uzi Vishne^a ; ^{vishne@math.biu.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16K20
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：471
• 期：Complete
• 页码：454-479
• 全文大小：493 K

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  -sub-bisets of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931630285X&_mathId=si1.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=c4082f071a3b25df4d01375045348ab4" title="Click to view the MathML source">G=Gal(L/F)class="mathContainer hidden">class="mathCode">$G=\mathrm{Gal}(L/F)$, where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931630285X&_mathId=si2.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=8122aed7b306557ece5d8b044a5c5b15" title="Click to view the MathML source">F=Cent(A)class="mathContainer hidden">class="mathCode">$F=\mathrm{Cent}(A)$, L   is the Galois closure of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931630285X&_mathId=si3.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=cbc8220786e49e3dcf935a6e9088e1e8" title="Click to view the MathML source">K/Fclass="mathContainer hidden">class="mathCode">$K/F$, and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931630285X&_mathId=si4.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=e757791c6c1b0761ffdd4f4b4c60bdae" title="Click to view the MathML source">H=Gal(L/K)class="mathContainer hidden">class="mathCode">$H=\mathrm{Gal}(L/K)$. This leads to a combinatorial interpretation of the growth of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931630285X&_mathId=si5.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=ccbb0e680fdab58469922bd22ae11230" title="Click to view the MathML source">dim_K⁡((KaK)ⁱ)class="mathContainer hidden">class="mathCode">${\dim }_K({(KaK)}^i)$, for fixed class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931630285X&_mathId=si52.gif&_user=111111111&_pii=S002186931630285X&_rdoc=1&_issn=00218693&md5=edb08b60ca88e1526634a648c51c0c04" title="Click to view the MathML source">a∈Aclass="mathContainer hidden">class="mathCode">$a\in A$, especially in terms of Kummer subspaces.