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AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS
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 Title & Authors
AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS
Elavarasan, Balasubramanian; Porselvi, Kasi;
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 Abstract
The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by (P), and characterize its diameter.
 Keywords
posets;semi-ideals;prime semi-ideals;zero-divisor graph;
 Language
English
 Cited by
1.
Poset Properties Determined by the Ideal - Based Zero-divisor Graph,;;

Kyungpook mathematical journal, 2014. vol.54. 2, pp.197-201 crossref(new window)
1.
Normal subgroup based power graphs of a finite group, Communications in Algebra, 2016  crossref(new windwow)
2.
Poset Properties Determined by the Ideal - Based Zero-divisor Graph, Kyungpook mathematical journal, 2014, 54, 2, 197  crossref(new windwow)
 References
1.
D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434-447. crossref(new window)

2.
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226. crossref(new window)

3.
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North-Holland, Amsterdam, 1976.

4.
R. Engelking, General Topology, Heldermann-Verlag, 2000.

5.
R. Halas, On extensions of ideals in posets, Discrete Math. 308 (2008), no. 21, 4972-4977. crossref(new window)

6.
R. Halas and M. Jukl, On Beck's coloring of posets, Discrete Math. 309 (2009), no. 13, 4584-4589. crossref(new window)

7.
V. Joshi, Zero divisor graph of a poset with respect to an ideal, Order: DOI 10.1007/s11083-011-9216-2. crossref(new window)

8.
J. R. Munkres, Topology, Prentice-Hall of Indian, New Delhi, 2005.

9.
S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003), no. 9, 4425-4443. crossref(new window)

10.
P. V. Venkatanarasimhan, Semi-ideals in posets, Math. Ann. 185 (1970), 338-348. crossref(new window)