MATH 436 Notes: Ideals
نویسنده
چکیده
An ideal K of R is a subset that is both a left ideal and a right ideal of R. For emphasis, we sometimes call it a two-sided ideal but the reader should understand that unless qualified, the word ideal will always refer to a two-sided ideal. The zero ideal (0) and the whole ring R are examples of two-sided ideals in any ring R. A (left)(right) ideal I such that I 6= R is called a proper (left)(right) ideal of R. Note in a commutative ring, left ideals are right ideals automatically and vice-versa. Also note that any type of ideal is a subring without 1 of the ring. However the converse is not true, for example Z is a subring of Q but not an ideal.
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