Prime bi-interior $Gamma $-ideals of TG-semring
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Abstract
The notation of prime bi-interior ideal, semi prime bi-interior ideal, irreducible bi-interior ideal and strongly prime
bi-interior ideal of TG-Semi ring (ternary gamma semi-ring) are introduced. We study properties of these ideals
and relations between them and also characterize regular TG-Semi-ring and TG-Semi-ring using prime bi-interior
ideals, irreducible and strongly irreducible bi-interior ideals in this article.
Keywords:
TGS, bi-interior ideal, prime ideals, prime bi-interior ideal, strong prime bi-interior ideal, semi prime bi-interior ideal and irreducible and strongly irreducible bi-interior idealsMathematics Subject Classification:
Mathematics- Pages: 542-546
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
P.J. Allen, A fundamental theorem of homomorphism for semi groups, Proc. Amer: Math. Soc., 21(1969), 412-420.
Pooth.G.L and Groenewald. N.I On prime One sided Bi-ideals and Quasi- ideals of a $Gamma$ Ring, Jour. Astral.Math.Soc., 53(1)(1992), 55-63,
Dutta .T.K. and Sardar. S.K., Semi-prime Ideals and Irreducible Ideals of $Gamma$-semi rings. NOVI SAD.J.Math., $30(1)(2000), 97-108$.
R. A. Good and D. R. Hughes, Associated groups for a semi group, Pull. Amer. Math. Soc., 58(1952), 624-625.
M. Henriksen, Ideals in semi rings with commutative addition, Amer. Math. Soc. Notices, 5(1958), 321-328.
K. Iseki, Quasi-ideals in semi rings without zero, Proc. Japan Acad., 34(1958), 79-84.
K. Iseki, Ideal theory of semi rings, Proc. Japan Acad., $32(1956), 554-559$.
K. Iseki, Ideal in semi rings, Proc. Japan Acad., 34(1958), 29.31.
Good. R.A and Hughes D.R. Associated Groups for a Semi group, Pull. Amer. Math. Soc., 58(1952), 624-625.
Iseki. K. Ideal Theory of semi ring. Proc. Japan Acad., $32(8)(1956), 554-559$.
Iseki.K. Ideal in semi ring. Proc.Japan Acad., $34(1)(1958), 29-31$.
R. D. Jagatap, Y.S. Pawar, Quasi-ideals and minimal quasi-ideals in $Gamma$-semi rings, Novi Sad J. Math., $39(2)(2009), 79-87$.
Lajos S, On the BI-ideals in semi groups, Proc. Japan Acad., 45(1969), 710-712.
S. Lajos and F. A. Szasz, On the Bi-ideals in associative ring, Proc. Japan Acad., 46(1970), 505-507.
Lajos S , Generalized ideals in semigroups, Acta. Sci. Math. Szeged., 22(1961), 217-222.
M. Murali Krishna Rao, $Gamma$ semirings-I, Southeast Asian Bull. Math. 19(1)(1995), 49-54.
M. Murali Krishna Rao, Г-semirings-II, Southeast Asian Bulletin of Mathematics, 21(3)(1997), 281-287.
M.Murali Krishna Rao, The Jacobson radical of $Gamma$ semiring, South East Asian Bulletin of Mathematics, 23(1999), 127-134.
M. Murali Krishna Rao, $Gamma$ semiring with identity, Discussiones Mathematicae General Algebra and Applications, 37(2017), 189207 ,
M.Murali Krishna Rao, Ideals in ordered $Gamma$ semirings, Discussiones Mathematicae General Algebra and Applications, 38(2018), 47-68.
M. Murali Krishna Rao, Bi-interior Ideals in semigroups, Discussiones Mathematicae General Algebra and Applications, $38(2018)$, 69-78.
M. Murali Krishna Rao, Left Bi-quasi ideals of semirings, Bull. Int.Math. Virtual Inst, 8(2018), 45-53.
M. Murali Krishna Rao. BI-quasi-ideals and fuzzy Biquasi ideals of Gamma- semi- group. Bull. Int. Math. Virtual Inst., 7(2)(2017), 231-242.
M. Murali Krishna Rao, P. Venkateswarlu and N.Rafi, Left Bi-quasi-ideals of Gamma- semirings, Asia Pacific Journal of Mathematics, 4(2)(2017), 144-153.
Shabir. M, and Kanwal. N, Prime Bi-ideals in semi group, Southeast Asian Bulletin of Mathematics, 31(2007), 757764.
O. Steinfeld, Uher die quasi ideals, Von halP gruppend Publ. Math, De Pre-cen, 4(1956), 262-275.
U. M. Swamy and K. L. N. Swamy, Fuzzy prime ideals of rings, Jour. Math. Anal. Appl., 134(1988), 94-103.
H. S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer: Math. Soc.(N.S.), 40(1934), 914-920.
G.Srinivasa Rao, D.Madhusudhana Rao, P-Pseudo Symmetric Ideals in Ternary Semi ring, IOSR Journal of Math ematics, 11(1)(2015), 105-111.
G.Srinivasa Rao, D.Madhusudhana Rao, Characterstics of Ternary Semi rings, International Journal of Engineering Research And Management, 2(1), 3-6.
G.Srinivasa Rao, D.Madhusudhanarao and P.Siva Prasad, Simple Ternary Semi-rings, The Global Journal of Mathematics & Mathematical Sciences, 9(2)(2016), 185-196.
G.Srinivasa Rao, D.Madhusudhana Rao, P.Siva Prasad and M.Vasantha, Ideals in Quotient Ternary Semi-rings, International Journal of Advanced in Management, Tech nology and Engineering Sciences, 7(12)(2017), 126-134.
G.Srinivasa Rao and D.Madhusudhana Rao, Structure of Ideals in Ternary Semi-rings.
G.Srinivasa Rao and D.Madhusudhana Rao, A Study on Ternary Semi-rings, International Journal of Mathematical Archive, 2014.
M.Sajani Lavanya, D.Madhusudhana Rao and V.Syam Julius Rajendra, Prime Biternary-Ideals in ternarySemirings, British Journal of Research, 2(6)(2015), 156 166.
D.Madhusudhana Rao, G.Srinivasa Rao, Special Elements in ternary semi rings, International Journal of Engineering Research and Applications, 4(11)(2014), 123-130.
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