moduleswhose

Moduleswhose is not a recognized term in standard mathematical literature on module theory. There is no established definition or canonical object known by this name, and it does not appear as a standard concept in widely cited references. If encountered as a single word in a source, it is usually either a typographical error or a fragment of a larger phrase such as “modules whose property P holds” or “modules over a ring R.” In formal writing, such a phrase should be rewritten to make the intended meaning explicit.

Possible interpretations include treating it as a shorthand for a class of modules defined by a property. For example, one might mean the class of modules whose annihilator has a given form, or the class of modules whose submodules satisfy a particular condition. However, without an explicit definition, these are only hypothetical interpretations and do not constitute a standard notion.

If a writer intends to introduce a term called "moduleswhose" as a new concept, the term should be defined precisely at its first appearance. A typical approach is to specify a property P and define the class M = { M | P(M) holds }, followed by examples and basic properties. For instance, one could define “moduleswhose annihilator is principal” or “moduleswhose submodules form a chain,” and then study their structural features, examples, and any relevant theorems. Absent such a definition, no general theory or catalogue of results can be attached to the term.

In summary, "moduleswhose" does not designate a standard mathematical object. Clear definition and explicit context are required for any meaningful discussion or citation in algebra.