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TOTAL GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO IDENTITY-SUMMAND ELEMENTS
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 Title & Authors
TOTAL GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO IDENTITY-SUMMAND ELEMENTS
Atani, Shahabaddin Ebrahimi; Hesari, Saboura Dolati Pish; Khoramdel, Mehdi;
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 Abstract
Let R be an I-semiring and S(R) be the set of all identity-summand elements of R. In this paper we introduce the total graph of R with respect to identity-summand elements, denoted by T(), and investigate basic properties of S(R) which help us to gain interesting results about T() and its subgraphs.
 Keywords
I-semiring;minimal prime co-ideal;identity-summand graph;total identity-summand graph;
 Language
English
 Cited by
1.
TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL,;;;

대한수학회지, 2015. vol.52. 1, pp.159-176 crossref(new window)
2.
THE ANNIHILATOR IDEAL GRAPH OF A COMMUTATIVE RING,;;;;

대한수학회지, 2015. vol.52. 2, pp.417-429 crossref(new window)
1.
TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL, Journal of the Korean Mathematical Society, 2015, 52, 1, 159  crossref(new windwow)
2.
THE ANNIHILATOR IDEAL GRAPH OF A COMMUTATIVE RING, Journal of the Korean Mathematical Society, 2015, 52, 2, 417  crossref(new windwow)
 References
1.
A. Abbasi and S. Habibi, The total graph of a commutative ring with respect to proper ideals, J. Korean Math. Soc. 49 (2012), no. 1, 85-98. crossref(new window)

2.
S. Akbari, D. Kiani, F. Mohammadi, and S. Moradi, The total graph and regular graph of a commutative ring, J. Pure Appl. Algebra 213 (2009), no. 12, 2224-2228. crossref(new window)

3.
D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008), no. 7, 2706-2719. crossref(new window)

4.
D. F. Anderson and A. Badawi, On the total graph of a commutative ring without the zeoro element, J. Algebra Appl. 11 (2012), no. 4, 1250074, 18 pp. crossref(new window)

5.
D. F. Anderson and A. Badawi, The generalized total graph of a commutative ring, J. Algebra Appl. 12 (2013), no. 5, 1250212, 18 pp. crossref(new window)

6.
D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative rings, J. Algebra 217 (1999), no. 2, 434-447. crossref(new window)

7.
T. Asir and T. Chelvam, The intersection graph of gamma sets in the total graph II, J. Algebra Appl. 12 (2013), no. 4, 1250199, 18 pp. crossref(new window)

8.
M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison Wesley Publishing Company, 1969.

9.
M. Axtell, J. Coykendall, and J. Stickles, Zero-divisor graphs of polynomials and power series over commutative rings, Comm. Algebra 33 (2005), no. 6, 2043-2050. crossref(new window)

10.
Z. Barati, K. Khashyarmanesh, F. Mohammadi, and K. Nafar, On the associated graphs to a commutative ring, J. Algebra Appl. 12 (2013), 1250184. crossref(new window)

11.
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226. crossref(new window)

12.
A. Bondy and U. S. R. Murty, Graph Theory, Graduate Texts in Mathematics, 244. Springer, New York, 2008.

13.
T. Chelvam and T. Asir, On the total graph and its complement of a commutative ring, Comm. Algebra 41 (2013), no. 10, 3820-3835. crossref(new window)

14.
T. Chelvam and T. Asir, The intersection graph of gamma sets in the total graph I, J. Algebra Appl. 12 (2013), 1250198, 18 pp. crossref(new window)

15.
S. Ebrahimi Atani, The zero-divisor graph with respect to ideals of a commutative semiring, Glas. Mat. Ser. III 43(63) (2008), no. 2, 309-320. crossref(new window)

16.
S. Ebrahimi Atani, An ideal-based zero-divisor graph of a commutative semiring, Glas. Mat. Ser. III 44(64) (2009), no. 1, 141-153. crossref(new window)

17.
S. Ebrahimi Atani, S. Dolati Pish Hesari, and M. Khoramdel, Strong co-ideal theory in quotients of semirings, J. Adv. Res. Pure Math. 5 (2013), no. 3, 19-32. crossref(new window)

18.
S. Ebrahimi Atani, The identity-summand graph of commutative semirings, J. Korean Math. Soc. 51 (2014), no. 1, 189-202. crossref(new window)

19.
S. Ebrahimi Atani and F. Esmaeili Khalil Saraei, The total graph of a commutative semiring, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 21 (2013), no. 2, 21-33.

20.
S. Ebrahimi Atani and S. Habibi, The total torsion element graph of a module over a commutative ring, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 19 (2011), no. 1, 23-34.

21.
S. Ebrahimi Atani and A. Yousefian Darani, Zero-divisor graphs with respect to primal and weakly primal ideals, J. Korean Math. Soc. 46 (2009), no. 2, 313-325. crossref(new window)

22.
J. S. Golan, Semirings and Their Applications, Kluwer Academic Publishers Dordrecht, 1999.

23.
J. Kist, Minimal Prime Ideals In Commutative Semigroups, Proc. Lond. Math. Soc. (3) 13 (1963), 31-50.

24.
H. Wang, On rational series and rational language, Theoret. Comput. Sci. 205 (1998), no. 1-2, 329-336.