FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2091399863> ?p ?o ?g. }

• W2091399863 endingPage "308" @default.
• W2091399863 startingPage "293" @default.
• W2091399863 abstract "Let <italic>F</italic> be a mixed free algebra on a set <italic>X</italic> over the field <italic>K</italic>. Let <italic>U</italic>, <italic>V</italic> be two ideals of <italic>F</italic>, and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartSet delta left-parenthesis x right-parenthesis comma left-parenthesis x element-of upper X right-parenthesis EndSet> <mml:semantics> <mml:mrow> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:mi>δ<!-- δ --></mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{ delta (x),(x in X)}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a basis for a free <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper F slash upper U comma upper F slash upper V right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>F</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>U</mml:mi> <mml:mo>,</mml:mo> <mml:mi>F</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>V</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(F/U,F/V)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-bimodule <italic>T</italic>. Then the map <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=x right-arrow Start 2 By 2 Matrix 1st Row 1st Column x plus upper V 2nd Column a m p semicolon 0 2nd Row 1st Column delta left-parenthesis x right-parenthesis 2nd Column a m p semicolon x plus upper U EndMatrix> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mtable rowspacing=4pt columnspacing=1em> <mml:mtr> <mml:mtd> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:mi>V</mml:mi> </mml:mrow> </mml:mtd> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:mn>0</mml:mn> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>δ<!-- δ --></mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:mtd> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:mi>U</mml:mi> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>x to (begin {array}{*{20}{c}} {x + V} & 0 {delta (x)} & {x + U} end {array} )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> induces an injective homomorphism <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F slash upper U upper V right-arrow Start 2 By 2 Matrix 1st Row 1st Column upper F slash upper V 2nd Column a m p semicolon 0 2nd Row 1st Column upper T 2nd Column a m p semicolon upper F slash upper U EndMatrix> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>U</mml:mi> <mml:mi>V</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mtable rowspacing=4pt columnspacing=1em> <mml:mtr> <mml:mtd> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>F</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> </mml:mtd> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:mn>0</mml:mn> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd> <mml:mi>T</mml:mi> </mml:mtd> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>F</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>F/UV to (begin {array}{*{20}{c}} {F/V} & 0 T & {F/U} end {array} )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. If <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F slash upper U> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>F/U</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F slash upper V> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>F/V</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are embeddable in matrices over a commutative algebra, so is <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F slash upper U upper V> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>U</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>F/UV</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Some special cases are investigated and it is shown that a PI algebra with nilpotent radical satisfies all identities of some full matrix algebra." @default.
• W2091399863 created "2016-06-24" @default.
• W2091399863 creator A5044812520 @default.
• W2091399863 date "1974-01-01" @default.
• W2091399863 modified "2023-10-17" @default.
• W2091399863 title "A matrix representation for associative algebras. I" @default.
• W2091399863 cites W1966778897 @default.
• W2091399863 cites W1973722201 @default.
• W2091399863 cites W1986906435 @default.
• W2091399863 cites W1987330815 @default.
• W2091399863 cites W2060063187 @default.
• W2091399863 cites W2061732958 @default.
• W2091399863 cites W2065388809 @default.
• W2091399863 cites W2069496097 @default.
• W2091399863 cites W2081300931 @default.
• W2091399863 cites W2083662759 @default.
• W2091399863 cites W2151469567 @default.
• W2091399863 cites W2313637748 @default.
• W2091399863 cites W2332837831 @default.
• W2091399863 cites W4256212512 @default.
• W2091399863 doi "https://doi.org/10.1090/s0002-9947-1974-0338081-5" @default.
• W2091399863 hasPublicationYear "1974" @default.
• W2091399863 type Work @default.
• W2091399863 sameAs 2091399863 @default.
• W2091399863 citedByCount "83" @default.
• W2091399863 countsByYear W20913998632012 @default.
• W2091399863 countsByYear W20913998632013 @default.
• W2091399863 countsByYear W20913998632014 @default.
• W2091399863 countsByYear W20913998632015 @default.
• W2091399863 countsByYear W20913998632016 @default.
• W2091399863 countsByYear W20913998632017 @default.
• W2091399863 countsByYear W20913998632018 @default.
• W2091399863 countsByYear W20913998632019 @default.
• W2091399863 countsByYear W20913998632020 @default.
• W2091399863 countsByYear W20913998632021 @default.
• W2091399863 countsByYear W20913998632022 @default.
• W2091399863 crossrefType "journal-article" @default.
• W2091399863 hasAuthorship W2091399863A5044812520 @default.
• W2091399863 hasBestOaLocation W20913998631 @default.
• W2091399863 hasConcept C11413529 @default.
• W2091399863 hasConcept C154945302 @default.
• W2091399863 hasConcept C33923547 @default.
• W2091399863 hasConcept C41008148 @default.
• W2091399863 hasConceptScore W2091399863C11413529 @default.
• W2091399863 hasConceptScore W2091399863C154945302 @default.
• W2091399863 hasConceptScore W2091399863C33923547 @default.
• W2091399863 hasConceptScore W2091399863C41008148 @default.
• W2091399863 hasIssue "0" @default.
• W2091399863 hasLocation W20913998631 @default.
• W2091399863 hasOpenAccess W2091399863 @default.
• W2091399863 hasPrimaryLocation W20913998631 @default.
• W2091399863 hasRelatedWork W1974891317 @default.
• W2091399863 hasRelatedWork W2007596026 @default.
• W2091399863 hasRelatedWork W2044189972 @default.
• W2091399863 hasRelatedWork W2061531152 @default.
• W2091399863 hasRelatedWork W2069964982 @default.
• W2091399863 hasRelatedWork W2313400459 @default.
• W2091399863 hasRelatedWork W2911598644 @default.
• W2091399863 hasRelatedWork W2913765211 @default.
• W2091399863 hasRelatedWork W4225152035 @default.
• W2091399863 hasRelatedWork W4245490552 @default.
• W2091399863 hasVolume "188" @default.
• W2091399863 isParatext "false" @default.
• W2091399863 isRetracted "false" @default.
• W2091399863 magId "2091399863" @default.
• W2091399863 workType "article" @default.