arXiv subjects

C L Wangneo

Publications and source records attributed to C L Wangneo.

2 recordsLinked to original sources

arXiv2025

Gabriel Quotient Rings

In this paper we prove the following theorem. Let R be a prime Noetherian ring with krull dimension |R| = n where n is a positive integer. Let Q be the Goldie quotient ring of R. For a fixed positive integer m < n, let xm be the set of all prime ideals of R such that krull dimension R/p equals m. Call xm the set of m-full prime ideals of R. Let Cm be the set of elements c of R With krull dimension R/cR less than m. Call g as the m-gabriel filter, if g is the family of right ideals I of R with krull dimension R/I less than m. We construct an extension ring R(m) of R having the following properties (i) R(m) is a subring of Q with identity element 1 of R. (ii) If u(R(m)) is the set of units of R(m) then u(R(m) intersection R equals the set cm. (iii) For a full set of m-prime ideals of R the set cm is a right ore set of R . We call R(m) as the m-Gabriel quotient ring of R.

math.RA↗

arXiv2016

On some conditions on a Noetherian ring

In this paper for a noetherian ring R with nilradical N we define semiprime ideals P and Q called as the left and right krull homogenous parts of N . We also recall the known definitions of localisability and the weak ideal invariance (w.i.i for short ) of an ideal of a noetherian ring R . We then state and prove results that culminate in our main theorem whose statement is given below ; Theorem :- Let R be a noetherian ring with nilradical N . Let P and Q be semiprime ideals of R that are the right and left krull homogenous parts of N respectively . Then the following conditions are equivalent ; (i) N is a right w.i.i ideal of R ( respectively N is a left w.i.i ideal of R ) . (ii)P is a right localizable ideal of R ( respectively Q is a left localizable ideal of R ) .

math.RA↗