Arbitrary algebras with a multiplicative basis

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• 作者：Antonio J. Calderó ; n Martí ; n ; ^{ajesus.calderon@uca.es" class="auth_mail" title="E-mail the corresponding author} ; Francisco J. Navarro Izquierdo ^{javi.navarroiz@uca.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A30 ; 15A21 ; 16xx ; 17Axx
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：498
• 期：Complete
• 页码：106-116
• 全文大小：300 K

文摘

Let g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si1.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=372b1e353d126750df80e8dc0ddea8d6" title="Click to view the MathML source">Agif" overflow="scroll">A be an algebra of arbitrary dimension, over an arbitrary base field g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si17.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=c5e77b887d5de32dab2c6c940ba3886b" title="Click to view the MathML source">Fgif" overflow="scroll">F and in which any identity on the product is not supposed. A basis g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si136.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=ce2901ecedda31d0a7202e73e6baa035" title="Click to view the MathML source">B={e_i}_i∈Igif" overflow="scroll">B={ei}i∈I of g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si1.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=372b1e353d126750df80e8dc0ddea8d6" title="Click to view the MathML source">Agif" overflow="scroll">A is called multiplicative if for any g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si33.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=03ff186b84ea1bce3bca7ca842898002" title="Click to view the MathML source">i,j∈Igif" overflow="scroll">i,j∈I we have that g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si5.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=a71dff597867d138f2382900fd2452d7" title="Click to view the MathML source">e_ie_j∈Fe_kgif" overflow="scroll">eiej∈Fek for some g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si133.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=367a75ca3073f1934b013256f92fb000" title="Click to view the MathML source">k∈Igif" overflow="scroll">k∈I. We show that if g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si1.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=372b1e353d126750df80e8dc0ddea8d6" title="Click to view the MathML source">Agif" overflow="scroll">A admits a multiplicative basis then it decomposes as the direct sum g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si22.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=715ab27e88c008f7798ac0e24c927412" title="Click to view the MathML source">A=⨁_kI_kgif" overflow="scroll">A=⨁kIk of well-described ideals admitting each one a multiplicative basis. Also the minimality of g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515000506&_mathId=si1.gif&_user=111111111&_pii=S0024379515000506&_rdoc=1&_issn=00243795&md5=372b1e353d126750df80e8dc0ddea8d6" title="Click to view the MathML source">Agif" overflow="scroll">A is characterized in terms of the multiplicative basis and it is shown that, under a mild condition, the above direct sum is by means of the family of its minimal ideals admitting a multiplicative basis.