Projectivity and flatness over the graded ring of normalizing elements
Let k be a field, H a cocommutative bialgebra, A a commutative left H-module algebra, Hom(H,A) the $k$-algebra of the k-linear maps from H to A under the convolution product, Z(H,A) the submonoid of Hom(H,A) whose elements satisfy the cocycle condition and G any subgroup of the monoid Z(H,A). We giv...
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/154259 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Projectivity and flatness over the graded ring of normalizing elements / T. Guédénon // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 172-192 . — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let k be a field, H a cocommutative bialgebra, A a commutative left H-module algebra, Hom(H,A) the $k$-algebra of the k-linear maps from H to A under the convolution product, Z(H,A) the submonoid of Hom(H,A) whose elements satisfy the cocycle condition and G any subgroup of the monoid Z(H,A). We give necessary and sufficient conditions for the projectivity and flatness over the graded ring of normalizing elements of A. When A is not necessarily commutative we obtain similar results over the graded ring of weakly semi-invariants of A replacing Z(H,A) by the set χ(H,Z(A)H) of all algebra maps from H to Z(A)H, where Z(A) is the center of A. |
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