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Amer. Math. Soc."],"abstract":"<p>We study the relations between partial and global group cohomology with values in a commutative unital ring <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper A\">\n  <mml:semantics>\n    <mml:mrow class=\"MJX-TeXAtom-ORD\">\n      <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">A<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\mathcal {A}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>. In particular, for a unital partial action of a group <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper G\">\n  <mml:semantics>\n    <mml:mi>G<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">G<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> on <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper A\">\n  <mml:semantics>\n    <mml:mrow class=\"MJX-TeXAtom-ORD\">\n      <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">A<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\mathcal {A}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>, such that <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper A\">\n  <mml:semantics>\n    <mml:mrow class=\"MJX-TeXAtom-ORD\">\n      <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">A<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\mathcal {A}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> is a direct product of commutative indecomposable rings, we show that any partial <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n  <mml:semantics>\n    <mml:mi>n<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>-cocycle of <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper G\">\n  <mml:semantics>\n    <mml:mi>G<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">G<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> with values in <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper A\">\n  <mml:semantics>\n    <mml:mrow class=\"MJX-TeXAtom-ORD\">\n      <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">A<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\mathcal {A}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> is globalizable.<\/p>","DOI":"10.1090\/tran\/8272","type":"journal-article","created":{"date-parts":[[2020,9,10]],"date-time":"2020-09-10T00:58:24Z","timestamp":1599699504000},"page":"1863-1898","source":"Crossref","is-referenced-by-count":1,"special_numbering":"1042","title":["Globalization of partial cohomology of groups"],"prefix":"10.1090","volume":"374","author":[{"given":"Mikhailo","family":"Dokuchaev","sequence":"first","affiliation":[]},{"given":"Mykola","family":"Khrypchenko","sequence":"additional","affiliation":[]},{"given":"Juan","family":"Sim\u00f3n","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2020,12,18]]},"reference":[{"key":"1","unstructured":"F. 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