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Why do we need left distibutivity when using semirings for shortest-path problems?

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#semiring
446
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Is there a less-trivial integer function with described properties?

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#functional-equations #integers #semiring
100
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The Tropical Semiring is Local?

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#abstract-algebra #commutative-algebra #semiring
47
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Can a collection of weighted graphs form a semiring?

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#abstract-algebra #graph-theory #semiring
161
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Is the absorbing property of semiring $S$ a necessary criteria for $S$ to be called semiring?

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#abstract-algebra #semiring
79
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Will kronecker product and usual matrix addition form semiring on the set of matrices?

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#matrices #semiring
149
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Do semirings always require neutral elements?

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#abstract-algebra #semiring
647
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What is the difference between semiring and hemiring?

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#ring-theory #semiring
52
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Can both additive and multiplicative operations in a semiring distribute over each other?

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#semiring
47
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Can a semiring other than monosemiring posses a common neutral element with respect to both the operations defined on it?

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#ring-theory #semiring
200
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Additive identity in a semiring need not be multiplicative annihilator.

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#ring-theory #semiring
59
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Examples of generalisations in which $k$-ring might be, for example, a monad ? What are $\textit{scalars}$, really?

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#category-theory #monads #scalar-fields #semiring
218
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$AB=I$ implies $BA=I$ in a $M_n(R)$ when $R$ is a semiring?

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#matrices #semiring
191
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About Semigroup & Semiring homomorphism

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#linear-algebra #group-theory #ring-theory #semigroups #semiring
38
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Semirings where all elements have only finitely many factors.

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#abstract-algebra #reference-request #ring-theory #semiring

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