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A Sheaf Representation for Modules with Applications to Gelfand Rings
Author(s) -
Borceux Francis,
Simmons Harold,
van den Bossche Gilberte
Publication year - 1984
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-48.2.230
Subject(s) - mathematics , sheaf , representation (politics) , pure mathematics , characterization (materials science) , algebra over a field , commutative property , politics , political science , law , materials science , nanotechnology
We give a new sheaf representation applicable to all rings and their modules. This representation extends the Pierce represtation, is a restriction of the Grothendieck representation in the commutative case, and agrees with the Mulvey representation for Gelfand rings. We give also a brief analysis of Gelfand rings including a new characterization of these rings.