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semirings [2010/07/29 18:30]
127.0.0.1 external edit
semirings [2019/03/14 16:46] (current)
jipsen
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==Morphisms== ==Morphisms==
Let $\mathbf{S}$ and $\mathbf{T}$ be semirings. A morphism from $\mathbf{S}$ Let $\mathbf{S}$ and $\mathbf{T}$ be semirings. A morphism from $\mathbf{S}$
-to $\mathbf{T}$ is a function $h:Sarrow T$ that is a homomorphism: +to $\mathbf{T}$ is a function $h:S\to T$ that is a homomorphism:
$h(x+y)=h(x)+h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$ $h(x+y)=h(x)+h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$
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$\begin{array}{lr} $\begin{array}{lr}
f(1)= &1\\ f(1)= &1\\
-f(2)= &1\\ +f(2)= &10\\ 
-f(3)= &\\ +f(3)= &132\\ 
-f(4)= &\\+f(4)= &2341\\
f(5)= &\\ f(5)= &\\
f(6)= &\\ f(6)= &\\
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====Subclasses==== ====Subclasses====
[[Idempotent semirings]] [[Idempotent semirings]]
 +
 +[[Semirings with identity]]
 +
 +[[Semirings with zero]]
====Superclasses==== ====Superclasses====