A Survey of Rings Generated by Units

Ashish K. Srivastava[1]

  • [1] Department of Mathematics and Computer Science, St. Louis University, St. Louis, MO-63103, USA

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: S1, page 203-213
  • ISSN: 0240-2963

Abstract

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This article presents a brief survey of the work done on rings generated by their units.

How to cite

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Srivastava, Ashish K.. "A Survey of Rings Generated by Units." Annales de la faculté des sciences de Toulouse Mathématiques 19.S1 (2010): 203-213. <http://eudml.org/doc/115897>.

@article{Srivastava2010,
abstract = {This article presents a brief survey of the work done on rings generated by their units.},
affiliation = {Department of Mathematics and Computer Science, St. Louis University, St. Louis, MO-63103, USA},
author = {Srivastava, Ashish K.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {rings generated by units; sums of units; endomorphisms; von Neumann regular rings; right self-injective rings; injective modules; unit sum numbers; regular elements},
language = {eng},
month = {4},
number = {S1},
pages = {203-213},
publisher = {Université Paul Sabatier, Toulouse},
title = {A Survey of Rings Generated by Units},
url = {http://eudml.org/doc/115897},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Srivastava, Ashish K.
TI - A Survey of Rings Generated by Units
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/4//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - S1
SP - 203
EP - 213
AB - This article presents a brief survey of the work done on rings generated by their units.
LA - eng
KW - rings generated by units; sums of units; endomorphisms; von Neumann regular rings; right self-injective rings; injective modules; unit sum numbers; regular elements
UR - http://eudml.org/doc/115897
ER -

References

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  1. N. Ashrafi, P. Vámos, On the unit sum number of some rings, Quart. J. Math. 56 (2005), 1-12. Zbl1100.11036MR2124574
  2. V. P. Camillo, H. P. Yu, Exchange rings, units and idempotents, Comm. Alg. 22, 12 (1994), 4737-4749. Zbl0811.16002MR1285703
  3. A. W. Chatters, S. M. Ginn, Rings generated by their regular elements, Glasgow Math. J. 25 (1984), 1-5. Zbl0531.16007MR731473
  4. H. Chen, Exchange rings with artinian primitive factors, Algebras and Representation Theory, Vol. 2, No. 2 (1999), 201-207. Zbl0960.16009MR1702275
  5. G. Ehrlich, Unit-regular rings, Portugal Math. 27 (1968), 209-212. Zbl0201.03901MR266962
  6. J. W. Fisher, R. L. Snider, Rings generated by their units, J. Algebra 42 (1976), 363-368. Zbl0335.16014MR419510
  7. K. R. Goodearl, von-Neumann Regular Rings, Krieger Publishing Company, Malabar, Florida, 1991. Zbl0749.16001MR1150975
  8. B. Goldsmith, S. Pabst and A. Scott, Unit sum numbers of rings and modules, Quart. J. Math. Oxford (2), 49 (1998), 331-344. Zbl0933.16035MR1645560
  9. D. Handelman, Perspectivity and cancellation in regular rings, J. Algebra, 48 (1977), 1-16. Zbl0363.16009MR447329
  10. M. Henriksen, On a class of regular rings that are elementary divisor rings. Arch. Math. (Basel) 24 (1973), 133Ð141. Zbl0257.16015MR379574
  11. M. Henriksen, Two classes of rings generated by their units, J. Algebra 31 (1974), 182-193. Zbl0285.16009MR349745
  12. D. Khurana and A. K. Srivastava, Right Self-injective Rings in Which Each Element is Sum of Two Units, Journal of Algebra and its Applications, Vol. 6, No. 2 (2007), 281-286. Zbl1116.16033MR2316422
  13. D. Khurana and A. K. Srivastava, Unit Sum Numbers of Right Self-injective Rings, Bulletin of Australian Math. Soc., Vol. 75, No. 3 (2007), 355-360. Zbl1119.16029MR2331013
  14. S. Lang, Algebraic Number Theory, Graduate Texts in Mathematics, Springer, 1986. Zbl0601.12001MR1282723
  15. T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Springer, 1990. Zbl0728.16001MR1838439
  16. T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, Springer, 1998. Zbl0911.16001MR1653294
  17. C. Meehan, Unit sum numbers of abelian groups and modules, Ph.D. thesis, Dublin Institute of Technology, 2001. 
  18. R. Raphael, Rings which are generated by their units, J. Algebra 28 (1974), 199-205. Zbl0271.16013MR342554
  19. J. C. Robson, Sums of two regular elements, Glasgow Math. J. 25 (1984), 7-11. Zbl0531.16008MR731474
  20. L. A. Skornyakov, Complemented Modular Lattices and Regular Rings, Oliver & Boyd, Edinburgh, 1964. Zbl0156.04101MR169799
  21. Y. Utumi, On Continuous Regular Rings and Semisimple Self-injective Rings, Canad. J. Math. 12 (1960), 597-605. Zbl0100.26303MR117250
  22. P. Vámos, 2-Good Rings, The Quart. J. Math. 56 (2005), 417-430. Zbl1156.16303MR2161255
  23. Z. Wang, J. L. Chen, To appear in the Canad. Math. Bull. MR2494320
  24. K. G. Wolfson, An ideal theoretic characterization of the ring of all linear transformations, Amer. J. Math. 75 (1953), 358-386. Zbl0050.11503MR53080
  25. D. Zelinsky, Every Linear Transformation is Sum of Nonsingular Ones, Proc. Amer. Math. Soc. 5 (1954), 627-630. Zbl0056.11002MR62728

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