Research and Innovation Articles
Published 2019-07-29
Keywords
- Unital ring,
- rings with enough idempotents,
- rings with sets of local units,
- locally unital ring,
- s-unital ring
- idempotent ring ...More
How to Cite
Nystedt, P. (2019). A survey of s-unital and locally unital rings. Revista Integración, Temas De matemáticas, 37(2), 251–260. https://doi.org/10.18273/revint.v37n2-2019003
Abstract
We gather some classical results and examples that show strict
inclusion between the families of unital rings, rings with enough idempotents, rings with sets of local units, locally unital rings, s-unital rings and idempotent rings.
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References
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Abrams G.D., Ara P. and Molina M. S., Leavitt Path Algebras, Springer Lecture Notes, London, 2017.
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Komatsu H., “The category of s-unital modules”, Math. J. Okayma univ. 28 (1986), No. 1, 65–91.
Lam T.Y., Exercises in classical ring theory, 2nd edition, Springer-Verlag, New York, 2003.
Lundström P., “Separable Groupoid Rings”, Comm. Algebra 34 (2006), 3029–3041.
Mogami I. and Hongan M., “Note on commutativity of rings”, Math. J. Okayama univ. 20 (1978), 21–24.
Tominaga H., “On decompositions into simple rings”, Math. J. Okayama univ. 17 (1975), No. 2, 159–163.
Tominaga H., “On s-unital rings”, Math. J. Okayama univ. 18 (1976), 117–134.
Abrams G.D., “Morita equivalence for rings with local units”, Comm. Algebra 11 (1983), No. 8, 801–837.
Abrams G.D., Ara P. and Molina M. S., Leavitt Path Algebras, Springer Lecture Notes, London, 2017.
Ánh P.N. and Márki L., “Morita equivalence for rings without identity”, Tsukuba J. Math. 11 (1987), No. 1, 1–16.
Fuller K.R., “On rings whose left modules are direct sums of finitely generated modules”, Proc. Amer. Math. Soc. 54 (1976), 39–44.
Komatsu H., “The category of s-unital modules”, Math. J. Okayma univ. 28 (1986), No. 1, 65–91.
Lam T.Y., Exercises in classical ring theory, 2nd edition, Springer-Verlag, New York, 2003.
Lundström P., “Separable Groupoid Rings”, Comm. Algebra 34 (2006), 3029–3041.
Mogami I. and Hongan M., “Note on commutativity of rings”, Math. J. Okayama univ. 20 (1978), 21–24.
Tominaga H., “On decompositions into simple rings”, Math. J. Okayama univ. 17 (1975), No. 2, 159–163.
Tominaga H., “On s-unital rings”, Math. J. Okayama univ. 18 (1976), 117–134.