IJPAM: Volume 113, No. 2 (2017)

Title

ON LINEARLY TOPOLOGIZED MODULES OVER
AN ARBITRARY RING

Authors

Patricia Couto G. Mauro$^1$, Dinamérico P. Pombo Jr.$^2$
$^1$Centro Interdisciplinar de Ciencias da Natureza
Universidade Federal da Integração Latino-Americana
Foz do Iguaçu, 85867-970, BRASIL
$^2$Instituto de Matemática e Estatística
Universidade Federal Fluminense
Niterói, 24020-140, BRASIL

Abstract

Fundamental constructions in the category of linearly topologized modules over an arbitrary ring are studied, as well as certain linearly topologized modules of multilinear mappings over an arbitrary commutative ring.

History

Received: January 14, 2017
Revised: March 3, 2017
Published: March 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 46M40, 46S10, 46G25, 46H99.
Key Words and Phrases: linearly topologized modules, continuous linear mappings, multilinear mappings.

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
N. Adasch, Über die Vollständigkeit von $L_{\sigma}(E,F)$, Math. Ann. 191 (1971), 290-292.

2
N. Bourbaki, Commutative Algebra, Hermann and Addison-Wesley, Paris and Reading (1972).

3
N. Bourbaki, Topological Vector Spaces, Springer-Verlag, Berlin - Heidelberg - New York (1987).

4
N. Bourbaki, Algebra I, Chapters 1-3, Second printing, Springer-Verlag, Berlin - Heidelberg (1989).

5
N. Bourbaki, General Topology, Chapters 1-4, Second printing, Springer-Verlag, Berlin - Heidelberg (1998).

6
N. Bourbaki, General Topology, Chapters 5-10, Second printing, Springer-Verlag, Berlin - Heidelberg (1998).

7
A. Grothendieck, Sur la complétion du dual d'un espace vectoriel localement convexe, C. R. Acad. Sci. Paris 230 (1950), 605-606.

8
A. Grothendieck & J. Dieudonné, Eléments de Géométrie Algébrique I Grundlehren der mathematischen Wissenschaften 166, Springer-Verlag, Berlin - Heidelberg - New York (1971).

9
G. Köthe, Topological Vector Spaces I, Grundlehren der mathematischen Wissenschaften 159, Springer-Verlag, Berlin - Heidelberg - New York (1969).

10
S. Lang, Algebra, Revised third edition, Graduate Texts in Mathematics 211, Springer-Verlag, Berlin - Heidelberg - New York (2002).

11
S. Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications XXVII, (1942), doi: https://doi.org/10.1090/coll/027.

12
P. C. G. Mauro & D. P. Pombo Jr., Linearly topologized modules over a discrete valuation ring, Boll. Unione Mat. Ital. 7 (2015), 253-278, doi: https://doi.org/10.1007/s40574-014-0015-8.

13
D. P. Pombo Jr., On the completion of certain topological modules, Math. Japonica 37 (1992), 333-336.

14
J. -P. Serre, A Course in Arithmetic, Third printing, Graduate Texts in Mathematics 7, Springer-Verlag, Berlin - Heidelberg - New York (1985).

How to Cite?

DOI: 10.12732/ijpam.v113i2.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 2
Pages: 345 - 368


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).