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ON THE STRUCTURE OF COMAXIMAL GRAPHS OF COMMUTATIVE RINGS WITH IDENTITY

Published online by Cambridge University Press:  26 November 2010

SLAVKO M. MOCONJA*
Affiliation:
University of Belgrade, Faculty of Mathematics, Studentski trg 16, Belgrade 11000, Serbia (email: slavko@matf.bg.ac.rs)
ZORAN Z. PETROVIĆ
Affiliation:
University of Belgrade, Faculty of Mathematics, Studentski trg 16, Belgrade 11000, Serbia (email: zoranp@matf.bg.ac.rs)
*
For correspondence; e-mail: slavko@matf.bg.ac.rs
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Abstract

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In this paper we investigate the center, radius and girth of comaximal graphs of commutative rings. We also provide some counterexamples to the results concerning the relation between isomorphisms of comaximal graphs and the rings in question. In addition, we investigate the relation between the comaximal graph of a ring and its subrings of a certain type.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This work was partially supported by Ministry of Science and Environmental Protection of Republic of Serbia Project #144018 and Project #144020.

References

[1]Atiyah, M. F. and Macdonald, I. G., Introduction to Commutative Algebra (Addison-Wesley, Reading, MA, 1969).Google Scholar
[2]Beck, I., ‘Coloring of commutative rings’, J. Algebra 116 (1988), 208226.CrossRefGoogle Scholar
[3]Maimani, H. R., Salimi, M., Sattari, A. and Yassemi, S., ‘Comaximal graph of commutative rings’, J. Algebra 319 (2008), 18011808.CrossRefGoogle Scholar
[4]Nikiforov, V., ‘Graphs with many copies of a given subgraph’, Electron. J. Combin. 15(1) (2008), # N6.Google Scholar
[5]Petrović, Z. Z. and Moconja, S. M., ‘On graphs associated to rings’, Novi Sad J. Math. 38(3) (2008), 3338.Google Scholar
[6]Redmond, S., ‘The zero-divisor graph of a non-commutative ring’, Internat. J. Commutative Rings 1(4) (2002), 203211.Google Scholar
[7]Sharma, P. D. and Bhatwadekar, S. M., ‘A note on graphical representation of rings’, J. Algebra 176 (1995), 124127.CrossRefGoogle Scholar
[8]Szigeti, J. and van Wyk, L., ‘Subrings which are closed with respect to taking the inverse’, J. Algebra 318 (2007), 10681076.CrossRefGoogle Scholar
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ON THE STRUCTURE OF COMAXIMAL GRAPHS OF COMMUTATIVE RINGS WITH IDENTITY
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