References
- N. Bourbaki, Commutative Algebra, Chapters 1-7, Elements of Mathematics, Springer, 1998.
- G. W. Chang and H. Kim, Divisibility properties of the semiring of ideals of an integral domain, Algebra Colloq., 27(3)(2020), 369-380. https://doi.org/10.1142/s1005386720000309
- M. Dehghanian and M. S. Modarres, Ternary γ-homomorphisms and ternary γ-derivations on ternary semigroups, J. Inequal. Appl., 34(2012).
- V. R. Daddi and Y. S. Pawar, On completely regular ternary semiring, Novi Sad J. Math., 42(2)(2012), 1-7.
- V. N. Dixit and S. Dewan, Minimal quasi-ideals in ternary semigroups, Indian J. Pure Appl. Math., 28(1997), 625-632.
- T. K. Dutta and S. Kar, On regular ternary semirings, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific (2003), 343-355.
- T. K. Dutta and S. Kar, A note on regular ternary semirings, Kyungpook Math. J., 46(2006), 357-365.
- T. K. Dutta, K. P. Shum and S. Mandal, Singular ideals of ternary semirings, Eur. J. Pure and Appl. Math., 5(2)(2012), 116-128.
- T. K. Dutta, S. Kar and K. Das, Power ternary semirings, Afr. Mat., 26(2015), 1483-1494. https://doi.org/10.1007/s13370-014-0300-9
- J. S. Golan, Semirings and their Applications, Springer Netherlands, 1999.
- N. Gubareni, Valuation and discrete valuation rings, Scientific Research of the Institute of Mathematics and Computer Science, 10(1)(2011), 61-70.
- U. Hebisch and H. J. Weinert, Semirings: Algebraic Theory and Applications in Computer Science, Series in Algebra, World Scientific, 1998.
- A. Iampan, Lateral ideals of ternary semigroups, Ukr. Math. Bull., 4(4)(2007), 525-534.
- S. Kar, On quasi-ideals and bi-ideals of ternary semirings, Int. J. Math. Math. Sci., 18(2005), 3015-3023. https://doi.org/10.1155/IJMMS.2005.3015
- S. Kar, Ideal theory in the ternary semiring ℤ-0, Bull. Malaya Math. Sci. Soc., (2)34(1)(2011), 69-77.
- S. Kar and A. Shikari, Soft ternary semirings, Fuzzy Inf. Eng., 8(1)(2016), 1-15. https://doi.org/10.1016/j.fiae.2016.03.001
- W. Krull, Allgemeine Bewertungstheorie, J. Reine Angew. Math., 167(1932), 160-196. https://doi.org/10.1515/crll.1932.167.160
- W. Krull, Beitrage zur Arithmetik kommutativer Integrittsbereiche. VI. Der allgemeine Diskrimminantensatz, Unverzweigte Ringerweiterungen Math. Z., 45(1939), 1-19. https://doi.org/10.1007/BF01580269
- M. Manis, Valuations on a commutative ring, Proc. Amer. Math Soc., 20(1969), 193-198. https://doi.org/10.1090/S0002-9939-1969-0233813-2
- P. Nasehpour, Valuation Semirings, J. Algebra Appl., 17(4)(2018), 1850073 (23 pages). https://doi.org/10.1142/S0219498818500731
- O. F. G. Schilling, Noncommutative valuations, Bull. Amer. Math. Soc., 51(1945), 297-304. https://doi.org/10.1090/S0002-9904-1945-08339-6
- G. Sheeja and S. Sri Bala, Congruences on ternary semigroups, Quasigroups Related Systems, 20(2012), 113-124.
- K. Valente, On orderings, valuations and 0-primes of a commutative ring, Rocky Mt. J. Math., 19(3)(1989), 973-984. https://doi.org/10.1216/RMJ-1989-19-3-973
- O. Zariski and P. Samuel, Commutative Algebra Vol. II, D. Van Nostrand Company, Inc. (1960).