A matrix M is usually called a hollow matrix if all of its diagonal elements are zero:

$$ M_{pp} = 0, \quad \forall \: p. $$

We can generalize this to an $n$-way tensor T, such that:

$$ T_{p_1 \cdots p_n} = 0, \quad \mbox{if any} \: p_i = p_j \: (i \neq j). $$

I call these types of tensors hollow. Are there other names for these?

Edit: made the question more precise.

A matrix M is usually called a hollow matrix if all of its diagonal elements are zero:

$$ M_{pp} = 0, \quad \forall \: p. $$

We can generalize this to an $n$-way tensor T, such that:

$$ T_{p_1 \cdots p_n} = 0, \quad \mbox{if $p_i = p_j$ for some $i \ne j$}. $$

I call these types of tensors hollow. Are there other names for these?

Edit: made the question more precise.

A matrix M is usually called a hollow matrix if all of its diagonal elements are zero:

$$ M_{pp} = 0, \quad \forall \: p. $$

We can generalize this to an $n$-way tensor T, such that:

$$ T_{p_1 \cdots p_n} = 0, \quad if \: p_i = p_j \: (i \neq j). $$

I call these types of tensors hollow. Are there other names for these?

A matrix M is usually called a hollow matrix if all of its diagonal elements are zero:

$$ M_{pp} = 0, \quad \forall \: p. $$

We can generalize this to an $n$-way tensor T, such that:

$$ T_{p_1 \cdots p_n} = 0, \quad \mbox{if any} \: p_i = p_j \: (i \neq j). $$

I call these types of tensors hollow. Are there other names for these?

Edit: made the question more precise.