I am a math Hobbyist reading Hungerford's book - Abstract Algebra (2nd Edition). In Chapter 6 on Ideals and Quotient Rings he writes (page 138 - see attached copies of pages 137 and 138 for context - whch is Finitely Generated Ideals):

"Theorem 6.3: Let R be a commutative ring with identity and , , ... ... , R.

Then the set I = { + + ... ... | , , ... ... , R} is an ideal in R"

I am trying to get a sense of the elements in the ideal in the Theorem above.

Are the elements always the sum of n non-zero elements and thus strictly of the form + + ... ... with no terms zero, or does the ideal contain (as I suspect) terms of the form with all other terms of the sum zero, + with all other terms zero, etc as well as the terms containing the sum of n elements.

Bernhard

Latex note: in the sum + I tried to make the subscripts 2 and 7 but for some reason Latex came up with an error every time I tried subscripts greater than 2!