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Thread: Terminology for elements in modules

  1. #1
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    Terminology for elements in modules

    I am looking for an adjective for special elements in modules.

    Definition: Let $\displaystyle R$ be a ring and $\displaystyle M$ be an $\displaystyle R$-module.
    We say that $\displaystyle v\in M$ is an ????? element if $\displaystyle v=rw$
    with $\displaystyle w\in M$ and $\displaystyle r\in R$ implies that $\displaystyle r$ has to be a unit in $\displaystyle R$.

    What is the commonly used term ???? for this definition?

    In the lattice case $\displaystyle R=\mathbb Z$ and $\displaystyle M=\mathbb Z^N$ these are often called
    primitive vectors but this terminology does not seem to be common
    for general rings and modules.


    Thanks ---
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  2. #2
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    Quote Originally Posted by crwtom View Post
    I am looking for an adjective for special elements in modules.

    Definition: Let $\displaystyle R$ be a ring and $\displaystyle M$ be an $\displaystyle R$-module.
    We say that $\displaystyle v\in M$ is an ????? element if $\displaystyle v=rw$
    with $\displaystyle w\in M$ and $\displaystyle r\in R$ implies that $\displaystyle r$ has to be a unit in $\displaystyle R$.

    What is the commonly used term ???? for this definition?

    In the lattice case $\displaystyle R=\mathbb Z$ and $\displaystyle M=\mathbb Z^N$ these are often called
    primitive vectors but this terminology does not seem to be common
    for general rings and modules.


    Thanks ---
    why is the terminology important here? if you have a "math" question related to this, you can ask.
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