simple

adjective

1. Uncomplicated; lacking complexity; taken by itself, with nothing added.
2. Easy; not difficult.
3. Without ornamentation; plain.
4. Free from duplicity; guileless, innocent, straightforward.
5. Undistinguished in social condition; of no special rank.
6. Trivial; insignificant.
7. Feeble-minded; foolish.
8. Consisting of one single substance; uncompounded.
9. Being non-trivial, and having no proper non-trivial normal subgroups (equivalently, no proper non-trivial quotient groups).
10. Being non-trivial, and having no proper non-trivial submodules (equivalently, no proper non-trivial quotient modules).
11. Being non-zero, and having no proper non-zero two-sided ideals (equivalently, no proper non-trivial quotient rings). For commutative rings, this definition coincides with that of a field.
12. Containing more than one element, and such that the only congruences on the structure are the diagonal relation (the equivalence relation a≡b⟺a=b) and the universal relation (the equivalence relation such that a≡b for all a,b). Equivalently, containing more than one element and having no proper non-trivial quotient algebras.
13. Being non-isomorphic to the terminal object, and such that its only quotient objects (up to isomorphism) are the terminal object and itself.
14. Being non-abelian and having no proper non-zero ideals. (Note that this is non-equivalent to the usual algebra sense; in particular, the abelian Lie algebra of dimension 1 over any given field is non-trivial and has no proper non-zero ideals, but is by convention not considered simple.)
15. Equal to a finite linear combination of indicator functions on measurable sets.
16. Not compound, but possibly lobed.
17. Using steam only once in its cylinders, in contrast to a compound engine, where steam is used more than once in high-pressure and low-pressure cylinders.
18. Consisting of a single individual or zooid; not compound.
19. Homogenous.
20. Mere; not other than; being only.