Mixing
How to think about this monoid?
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Let $P$ be a commutative monoid. Consider the $P$-monoid $P^{frac{1}{n}}$ which is any monoid isomorphic to the monoid $n:P to P$ ( $x to x^n$). I'm using the multiplicative notation for my monoids.
How to think about $P^{ frac{1}{n}}$ exactly? Suppose $P= mathbb{N}$. What is $mathbb{N}^{frac{1}{n}}$ exactly? Is it just $mathbb{N} cup { frac{x}{n}: x in mathbb{N} }$?
$M$ is a $P$-monoid if there is a monoid morphism from $P$ to $M$.
abstract-algebra monoid
asked Jan 17 at 0:12
grontimgrontim
325110
$endgroup$
add a comment |
$begingroup$
Let $P$ be a commutative monoid. Consider the $P$-monoid $P^{frac{1}{n}}$ which is any monoid isomorphic to the monoid $n:P to P$ ( $x to x^n$). I'm using the multiplicative notation for my monoids.
How to think about $P^{ frac{1}{n}}$ exactly? Suppose $P= mathbb{N}$. What is $mathbb{N}^{frac{1}{n}}$ exactly? Is it just $mathbb{N} cup { frac{x}{n}: x in mathbb{N} }$?
$M$ is a $P$-monoid if there is a monoid morphism from $P$ to $M$.
abstract-algebra monoid
asked Jan 17 at 0:12
grontimgrontim
325110
$endgroup$
1
$begingroup$
What is the definition of $P$-monoid?
$endgroup$
– Giorgio Mossa
Jan 17 at 9:39
$begingroup$
Although you wrote "I'm using the multiplicative notation for my monoids," the $mathbb N$ seems to be the additive monoid of natural numbers.
$endgroup$
– Andreas Blass
Jan 17 at 19:44
$begingroup$
Please clarify your question. What do you mean by "the monoid $n:P to P$ ( $x to x^n$)"? What is the underlying set of your monoid and how is the operation defined?
$endgroup$
– J.-E. Pin
Feb 12 at 11:29
add a comment |
$begingroup$
Let $P$ be a commutative monoid. Consider the $P$-monoid $P^{frac{1}{n}}$ which is any monoid isomorphic to the monoid $n:P to P$ ( $x to x^n$). I'm using the multiplicative notation for my monoids.
How to think about $P^{ frac{1}{n}}$ exactly? Suppose $P= mathbb{N}$. What is $mathbb{N}^{frac{1}{n}}$ exactly? Is it just $mathbb{N} cup { frac{x}{n}: x in mathbb{N} }$?
$M$ is a $P$-monoid if there is a monoid morphism from $P$ to $M$.
abstract-algebra monoid
asked Jan 17 at 0:12
grontimgrontim
325110
$endgroup$
Let $P$ be a commutative monoid. Consider the $P$-monoid $P^{frac{1}{n}}$ which is any monoid isomorphic to the monoid $n:P to P$ ( $x to x^n$). I'm using the multiplicative notation for my monoids.
How to think about $P^{ frac{1}{n}}$ exactly? Suppose $P= mathbb{N}$. What is $mathbb{N}^{frac{1}{n}}$ exactly? Is it just $mathbb{N} cup { frac{x}{n}: x in mathbb{N} }$?
$M$ is a $P$-monoid if there is a monoid morphism from $P$ to $M$.
abstract-algebra monoid
abstract-algebra monoid
asked Jan 17 at 0:12
grontimgrontim
325110
asked Jan 17 at 0:12
grontimgrontim
325110
edited Jan 17 at 17:34
grontim
asked Jan 17 at 0:12
grontimgrontim
325110
asked Jan 17 at 0:12
grontimgrontim
325110
asked Jan 17 at 0:12
grontimgrontim
325110
325110
1
$begingroup$
What is the definition of $P$-monoid?
$endgroup$
– Giorgio Mossa
Jan 17 at 9:39
$begingroup$
Although you wrote "I'm using the multiplicative notation for my monoids," the $mathbb N$ seems to be the additive monoid of natural numbers.
$endgroup$
– Andreas Blass
Jan 17 at 19:44
$begingroup$
Please clarify your question. What do you mean by "the monoid $n:P to P$ ( $x to x^n$)"? What is the underlying set of your monoid and how is the operation defined?
$endgroup$
– J.-E. Pin
Feb 12 at 11:29
add a comment |
1
$begingroup$
What is the definition of $P$-monoid?
$endgroup$
– Giorgio Mossa
Jan 17 at 9:39
$begingroup$
Although you wrote "I'm using the multiplicative notation for my monoids," the $mathbb N$ seems to be the additive monoid of natural numbers.
$endgroup$
– Andreas Blass
Jan 17 at 19:44
$begingroup$
Please clarify your question. What do you mean by "the monoid $n:P to P$ ( $x to x^n$)"? What is the underlying set of your monoid and how is the operation defined?
$endgroup$
– J.-E. Pin
Feb 12 at 11:29
1
1
$begingroup$
What is the definition of $P$-monoid?
$endgroup$
– Giorgio Mossa
Jan 17 at 9:39
$begingroup$
What is the definition of $P$-monoid?
$endgroup$
– Giorgio Mossa
Jan 17 at 9:39
$begingroup$
Although you wrote "I'm using the multiplicative notation for my monoids," the $mathbb N$ seems to be the additive monoid of natural numbers.
$endgroup$
– Andreas Blass
Jan 17 at 19:44
$begingroup$
Although you wrote "I'm using the multiplicative notation for my monoids," the $mathbb N$ seems to be the additive monoid of natural numbers.
$endgroup$
– Andreas Blass
Jan 17 at 19:44
$begingroup$
Please clarify your question. What do you mean by "the monoid $n:P to P$ ( $x to x^n$)"? What is the underlying set of your monoid and how is the operation defined?
$endgroup$
– J.-E. Pin
Feb 12 at 11:29
$begingroup$
Please clarify your question. What do you mean by "the monoid $n:P to P$ ( $x to x^n$)"? What is the underlying set of your monoid and how is the operation defined?
$endgroup$
– J.-E. Pin
Feb 12 at 11:29
add a comment |
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$begingroup$
What is the definition of $P$-monoid?
$endgroup$
– Giorgio Mossa
Jan 17 at 9:39
$begingroup$
Although you wrote "I'm using the multiplicative notation for my monoids," the $mathbb N$ seems to be the additive monoid of natural numbers.
$endgroup$
– Andreas Blass
Jan 17 at 19:44
$begingroup$
Please clarify your question. What do you mean by "the monoid $n:P to P$ ( $x to x^n$)"? What is the underlying set of your monoid and how is the operation defined?
$endgroup$
– J.-E. Pin
Feb 12 at 11:29