JOURNAL BROWSE
Search
Advanced SearchSearch Tips
TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL
Atani, Shahabaddin Ebrahimi; Hesari, Saboura Dolati Pish; Khoramdel, Mehdi;
  PDF(new window)
 Abstract
Let R be a semiring, I a strong co-ideal of R and S(I) the set of all elements of R which are not prime to I. In this paper we investigate some interesting properties of S(I) and introduce the total identity-summand graph of a semiring R with respect to a co-ideal I. It is the graph with all elements of R as vertices and for distinct x, , the vertices x and y are adjacent if and only if .
 Keywords
strong co-ideal;total identity-summand graph;identity-summand graph based a co-ideal;total identity-summand graph based a co-ideal;
 Language
English
 Cited by
 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.
D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008), no. 7, 2706-2719. crossref(new window)

3.
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)

4.
M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison Wesley Publishing Company, 1969.

5.
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226. crossref(new window)

6.
A. Bondy and U. S. R. Murty, Graph Theory, Graduate Texts in Mathematics, 244. Springer, New York, 2008.

7.
D. Dolzan and P. Oblak, The zero-divisor graphs of rings and semirings, Internat. J. Algebra Comput. 22 (2012), no. 4, 1250033, 20 pp. crossref(new window)

8.
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)

9.
S. Ebrahimi Atani, An ideal-based zero-divisor graph of a commutative semiring, Glas. Matematicki 44(64) (2009), 141-153. crossref(new window)

10.
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)

11.
S. Ebrahimi Atani, The Identity-Summand Graph of Commutative Semirings, J. Korean Math. Soc. 51 (2014), no. 1, 189-202. crossref(new window)

12.
S. Ebrahimi Atani, A co-ideal based identity-summand graph of a commutative semiring, submitted.

13.
S. Ebrahimi Atani, Total Graph of a Commutative semiring with respect to identity-summand elements, J. Korean Math. Soc. 51 (2014), no. 3, 593-607. crossref(new window)

14.
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.

15.
J. S. Golan, Semirings and Their Applications, Kluwer Academic Publishers Dordrecht, 1999.

16.
J. Kist, Minimal prime ideals in commutative semigroups, Proc. London Math. Soc. (3) 13 (1963), 31-50.

17.
H. Wang, On rational series and rational language, Theoret. Comput. Sci. 205 (1998), no. 1-2, 329-336. crossref(new window)