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Graded modules over object-unital groupoid graded rings
Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga (COL).
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga (COL).
2021 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 50, no 2, p. 444-462Article in journal (Refereed) Published
Abstract [en]

In this article, we analyze the category(Formula presented) of unitary G-graded modules over object unital G -graded rings R, being G a groupoid. Here we consider the forgetful functor  G - R- mod and determine many properties (Formula presented.) for which the following implications are valid for modules M in (Formula presented.) M is (Formula presented.) (Formula presented.) U(M) is (Formula presented.) U(M) is (Formula presented.) (Formula presented.) M is (Formula presented.) We treat the cases when (Formula presented.) is any of the properties: direct summand, projective, injective, free and semisimple. Moreover, graded versions of results concerning classical module theory are established, as well as some structural properties (Formula presented.). 

Place, publisher, year, edition, pages
Taylor & Francis Group, 2021. Vol. 50, no 2, p. 444-462
Keywords [en]
finitely gererated, finitely presented, free, groupoid graded module, injective, projective, pure sequences, small and flat modules, 16D10, 16D40, 16D50, 16D90
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:hv:diva-17455DOI: 10.1080/00927872.2021.1959601ISI: 000686088500001Scopus ID: 2-s2.0-85113240292OAI: oai:DiVA.org:hv-17455DiVA, id: diva2:1609568
Note

To see the correct formulas in the abstract; see the original article.

Available from: 2021-11-08 Created: 2021-11-08 Last updated: 2022-04-04Bibliographically approved

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Lundström, Patrik

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