Abstract
As previously mentioned, a semiring R is a nonempty set on which we have defined two operations, addition and multiplication, satisfying the following conditions:
-
(1)
(R, +) is a commutative monoid with identity element 0R;
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(2)
(R,·) is a monoid with identity element 1R;
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(3)
Multiplication distributes over addition from either side;
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(4)
$${0_{{R^r}}} = {0_R} = r{0_R}$$
for all r∈R;
-
(5)
0R ≠1R.
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© 1999 Springer Science+Business Media Dordrecht
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Golan, J.S. (1999). Background Material. In: Power Algebras over Semirings. Mathematics and Its Applications, vol 488. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9241-3_2
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DOI: https://doi.org/10.1007/978-94-015-9241-3_2
Publisher Name: Springer, Dordrecht
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