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Roland Coghetto

(2): 263-269, 1992. [6] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. [7] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. [8] D.F. Goguadze. About the notion of semiring of sets. Mathematical Notes, 74:346-351, 2003. ISSN 0001-4346. doi:10.1023/A:1026102701631. [9] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990. [10] Beata Padlewska. Families of sets. Formalized Mathematics, 1

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Mehmet Ali Öztürk

References 1. Barnes, W.E. - On the Γ-rings of Nobusawa, Pacific J. Math., 18 (1966), 411-422. 10.2140/pjm.1966.18.411 2. Genç, A. - The quotient rings of prime Γ-rings, (Asal Γ-halkalar_n_n kesirler halkaŞ), PhD Thesis, Ege University, Institute of Science, Bornova-İzmir, 2008. 3. Golan, J.S. - Semirings and Their Applications, Kluwer Academic Publishers, Dordrecht, 1999. 4. Dedekind, R. - Über die Theorie der ganzen algebraischen Zahlen, Supplement XI to P.G. Lejeune Dirichlet: Vorlesungen

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Sunil K. Maity and Rumpa Chatterjee

References [1] J.L. Galbiati and M.L. Veronesi, On quasi completely regular semigroups, Semigroup Forum 29 (1984) 271-275. doi: 10.1007/BF02573335 [2] J.M. Howie, Introduction to the theory of semigroups (Academic Press, 1976). [3] J.S. Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science (Pitman Monographs and Surveys in Pure and Applied Mathematics, 54, Longman Scientific, 1992). [4] M.K. Sen, S.K. Maity and K.P. Shum, On Completely Regular Semirings

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Marapureddy Murali Krishna Rao

References [1] T.K. Dutta and S. Kar, On regular ternary semirings, Advances in Algebra, Pro- ceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific, (2003) 343-355. [2] H. Lehmer, A ternary analogue of abelian groups, American J. Math. 59 (1932) 329-338. doi: 10.2307/2370997 [3] W.G. Lister, Ternary rings, Tran. Amer. Math. Soc. 154 (1971) 37-55. doi: 10.2307/1995425 [4] J. Hanumanthachari and K. Venuraju, The additive semigroup structure of semiring, Math

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Marapureddy Murali Krishna Rao

References [1] P.J. Allen, A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc. 21 (1969) 412-416. doi: 10.1090/S0002-9939-1969-2400237575-4241 [2] S.S. Ahn, Y.B. Jun and H.S. Kim, Ideals and quotients of incline algebras, Comm. Korean Math. Soc. 16 (2001) 2573-583. [3] S.S. Ahn and H.S. Kim, On r-ideals in incline algebras, Comm. Korean Math. Soc. 17 (2002) 229-235. [4] T.K. Dutta and S. Kar, On regular ternary semirings, Advances in algebra, Proceed- ings of the ICM

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Shahabaddin Ebrahimi Atani and Fatemeh Esmaeili Khalil Saraei

References [1] D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra, 159 (1993), 500-514. [2] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra, 320 (2008), 2706-2719. [3] D. F. Anderson and P. F. Livingston, The zero-divisor graph of a com- mutative ring, J. Algebra, 217 (1999), 437-447. [4] P. J. Allen, A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21 (1969), 412-416. [5] I. Beck

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Tapas Kumar Mondal and Anjan Kumar Bhuniya

References [1] A.K. Bhuniya, K. Jana, Bi-ideals in k-regular and intra k-regular semirings, Discussiones Mathematicae-General Algebra and Applications 31(2011) 5-25 [2] A.K. Bhuniya, T.K. Mondal, On the least distributive lattice congruence on a semiring with a semilattice additive reduct, Acta Mathematica Hungarica DOI: 10.1007/s10474-015-0526-5 [3] A.K. Bhuniya, T.K. Mondal, Distributive lattice decompositions of semirings with a semilattice additive reduct, Semigroup Forum 80(2010), 293-301 [4

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Marapureddy Murali Krishna Rao and B. Venkateswarlu

R eferences [1] R.A. Good and D.R. Hughes, Associated groups for a semigroup , Bull. Amer. Math. Soc. 58 (1952) 624-625. [2] M. Henriksen, Ideals in semirings with commutative addition , Amer. Math. Soc. Notices 5 (1958) 321. [3] K. Iseki, Quasi-ideals in semirings without zero , Proc. Japan Acad. 34 (1958) 79–84. doi:10.3792/pja/1195524783 [4] K. Iseki, Ideal theory of semiring , Proc. Japan Acad. 32 (1956) 554-559. doi:10.3792/pja/1195525272 [5] K. Iseki, Ideal in semirings , Proc. Japan Acad. 34 (1958) 29–31. doi:10

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M. Murali Krishna Rao and K.R. Kumar

References [1] P.J. Allen, A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc. 21 (1969) 412-416. doi: 10.1090/S0002-9939-1969-0237575-4 [2] S. Bourne and H. Zassenhaus, On the semiradical of a semiring, Proceedings N.A of S of USA 44 (1958) 907-914. [3] A.H. Clifford and D.D. Miller, Semigroups having zeroid elements, Amer. J. Math. 70 (1948) 117-125. doi: 10.1090/S0002-9904-1955-09895-1 [4] D.F. Dawson, Semigroups having left or right zeroid elements, Bolyai. Institute

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Hippolyte Hounnon

R eferences [1] K. Denecke and H. Hounnon, All solid varieties of semirings , J. Algebra 248 (2002) 107–117. doi:10.1006/jabr.2002.9023 [2] K. Denecke and H. Hounnon, All pre-solid varieties of semirings , Demonstratio Math. XXXVII (2004) 13–34. [3] K. Denecke and S.L. Wismath, Hyperidentities and Clones (Gordon and Breach Science Publishers, 2000). ISBN 9789056992354 [4] E. Graczyńska, On normal and regular identities , Algebra Universalis 27 (1990) 387–397. doi:10.1007/BF01190718 [5] U. Hebisch and H.J. Weinert, Semirings