Abstract
A semiring (R, +,•) is a nonempty set R on which we have defined operations of addition and multiplication satisfying the following conditions:
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(1)
(R, +) is a commutative monoid with identity element 0;
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(2)
(R, •) is a monoid with identity element 1 ≠ 0;
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(3)
a(b + c) = ab+ ac and (a + b)c — ac + bc for all a, b, c ∈ R;
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(4)
0a = 0 = a0 for all a ∈ R.
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© 2003 Springer Science+Business Media Dordrecht
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Golan, J.S. (2003). Semirings. In: Semirings and Affine Equations over Them: Theory and Applications. Mathematics and Its Applications, vol 556. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0383-3_1
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DOI: https://doi.org/10.1007/978-94-017-0383-3_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6310-6
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