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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154259 |
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| 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| _version_ | 1862735046281003008 |
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| author | Guédénon, T. |
| author_facet | Guédénon, T. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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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| first_indexed | 2025-12-07T19:46:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154259 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:46:50Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Guédénon, T. 2019-06-15T12:01:00Z 2019-06-15T12:01:00Z 2015 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. 1726-3255 2010 MSC:16D40, 16W50, 16W30. https://nasplib.isofts.kiev.ua/handle/123456789/154259 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. The author is grateful to the referee for his or her interesting remarksand helpful suggestions. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Projectivity and flatness over the graded ring of normalizing elements Article published earlier |
| spellingShingle | Projectivity and flatness over the graded ring of normalizing elements Guédénon, T. |
| title | Projectivity and flatness over the graded ring of normalizing elements |
| title_full | Projectivity and flatness over the graded ring of normalizing elements |
| title_fullStr | Projectivity and flatness over the graded ring of normalizing elements |
| title_full_unstemmed | Projectivity and flatness over the graded ring of normalizing elements |
| title_short | Projectivity and flatness over the graded ring of normalizing elements |
| title_sort | projectivity and flatness over the graded ring of normalizing elements |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154259 |
| work_keys_str_mv | AT guedenont projectivityandflatnessoverthegradedringofnormalizingelements |