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Jianming Zhan and B. Davvaz

(2011), 381-394. 15. Jun, Y.B. - On fuzzy prime ideals ofΓ-rings, Soochow J. Math., 21 (1995), 41-48. 16. Jun, Y.B.; Lee, C.Y. - Fuzzy Γ-rings, Pusan Kyongnam Math. J. (now, East Asian Math. J.), 8 (1992), 163-170. 17. Krasner, M. - A class of hyperrings and hyperfields, Internat. J. Math. Math. Sci., 6 (1983), 307-311. 18. Leoreanu Fotea, V.; Corsini, P. - Soft hypergroups, Critical Review. A publi-cation of Society for Mathematics of Uncertainty, Creighton University, USA, July 2010, vol. IV, 81-97. 19. Leoreanu-Fotea, V.; Davvaz, B. - Fuzzy

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M. Murali Krishna Rao and K.R. Kumar

Abstract

In this paper we introduce the notion of a left zeroid and a right zeroid of Γ -semirings. We prove that, a left zeroid of a simple Γ-semiring M is regular if and only if M is a regular Γ -semiring.

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Marapureddy Murali Krishna Rao

Abstract

In this paper we study the properties of structures of the semigroup (M,+) and the Γ-semigroup M of Γ -semiring M and regular Γ-semiring M satisfying the identity a + aαb = a or aαb + a = a or a + aαb + b = a or a + 1 = 1, for all a ∈ M, α ∈ Γ. We also study the properties of Γ-semiring with unity 1 which is also an additive identity.

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Hippolyte Hounnon

Abstract

The lattice of all regular-solid varieties of semirings splits in two complete sublattices: the sublattice of all idempotent regular-solid varieties of semirings and the sublattice of all normal regular-solid varieties of semirings. In this paper, we discuss the idempotent part.

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Marapureddy Murali Krishna Rao and B. Venkateswarlu

.3792/pja/1195524845 [6] R.D. Jagatap and Y.S. Pawar, Quasi-ideals and minimal quasi-ideals in Γ -semirings , Novi Sad J. Math. 39 (2009) 79–87. dmi.uns.ac.rs/nsjom/Papers/39-2/NSJOM-39-2-079-087.pdf. [7] S. Lajos, On the bi-ideals in semigroups , Proc. Japan Acad. 45 (1969) 710–712. doi:10.3792/pja/1195520625 [8] S. Lajos and F.A. Szasz, On the bi-ideals in associative ring , Proc. Japan Acad. 46 (1970) 505–507. doi:10.3792/pja/1195520265 [9] H. Lehmer, A ternary analogue of abelian groups , Amer. J. Math. 59 (1932) 329–338. doi:10

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Ivan Chajda and Helmut Länger

Abstract

Since the reduct of every residuated lattice is a semiring, we can ask under what condition a semiring can be converted into a residuated lattice. It turns out that this is possible if the semiring in question is commutative, idempotent, G-simple and equipped with an antitone involution. Then the resulting residuated lattice even satisfies the double negation law. Moreover, if the mentioned semiring is finite then it can be converted into a residuated lattice or join-semilattice also without asking an antitone involution on it. To a residuated lattice L which does not satisfy the double negation law there can be assigned a so-called augmented semiring. This can be used for reconstruction of the so-called core C(L) of L. Conditions under which C(L) constitutes a subuniverse of L are provided.

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Hvedri Inassaridze, Le Hoang Mai and Nguyen Xuan Tuyen

References [1] L. Marki, R. Mlitz and R. Wiegandt. A general Kurosh-Amitsur radical theory. Commun. Algebra, 16:249{305, 1988. [2] D. M. Olson and T. L. Jenkins. Radical theory for hemirings. J. Nature. Sci. Math., 23:23{32, 1983. [3] D. M. Olson and A. C. Nance. A note on radical for hemirings. Quaestiones Mathematicae, 12:307{314, 1989. [4] D. M. Olson, G. A. P. Heyman and L. H. LeRoux. Weakly special classes of hemirings. Quaestiones Mathematicae, 15:119{126, 1992. [5] D. M. Olson, L. H. LeRoux and G. A. P. Heyman. Three special classes for hemirings

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Archives of Control Sciences

The Journal of Polish Academy of Sciences

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Real Estate Management and Valuation

The Journal of Towarzystwo Naukowe Nieruchomosci

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Chemical and Process Engineering

The Journal of Committee of Chemical and Process of Polish Academy of Sciences