Topics in algebraic geometry

The dissertation begins in Chapter I with the basic properties of an algebral variety. The Hilbort Nulletellenesiz and its important consequenses are than given; the proofs of the results on dimension are greatly simplified by appealing to a result of the next chepter. In chapter II, the longth of a primary ideal is first discussed, preparatory to the ideas of height and depth of prime ideals. The fundamental equivalence between height and depth, and rans and dimension in a finite integral domain, is the last main theorem of this chapter. The simple point on a varlety is discussed in Chapter III form a local-algebraic point of view. It is shown that simplicity corresponds to regularity of the local ring, as defined by W. Krull. Finally the Jacobisn Oriterion for a simple point of a variety is established, and we montion the extension to algebraic subvarieties