Have any authors suggested mathematics-wide prefixes for "missing a quotient" and/or "missing an identity"?

Question

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation."

1. seminorm
2. pseudometric

Similarly, the prefixes in the following terms both mean: "missing identities"

1. semicategory
2. pseudoring

It would be nice if there was a prefix that could be used "mathematics wide" to mean "missing the identities," and another that could be used to mean "missing the obvious quotient by the obvious equivalence relation."

Question. Have any authors suggested such prefixes?