… a ring R has Krull dimension −1 if and only if it is trivial (ie, 1R = 0R). Since the notion of Krull
dimension is … elementary characterization of Krull dimension, without invoking prime ideals. …

… that the ring S⋄(M) has finite Krull dimension and we show that dimS⋄(M) equals the dimension
of … decomposition results, these rings are closer to polynomial rings than to the classical …

… ideals in ring theory. The current paper focuses on the resulting notion of Krull dimension, …
that an n variable polynomial ring over T , Z m a x or B always has dimension n larger than …

… such chain of $ n+ 2$ prime ideals, then we say that R has dimension n. The power series
ring $ R [[X]] $ may have infinite dimension even though R has finite dimension. References …

… that a semiprime ring with Krull dimension is a right order in a semisimple artinian ring, and
give … having a Krull dimension need not be inherited by a polynomial ring, having a Gabriel …

… We show that if $ A $ is a ring of Krull dimension $ d $ such … ring $ A $ which satisfies the
above conditions is necessarily an affine ring over $ k $ and is necessarily a polynomial ring if it …

… Let R be a commutative ring with identity and denote by dim R the Krull dimension of R. It is
… for polynomial rings cannot occur; that is, if P and Q are prime ideals of any ring R such that …

… Krull dimension in RH[x]. In this section, we study the Krull dimension of the Hurwitz polynomial
ring RH[… Hence, when studying the Krull dimension of RH[x], we may always assume that …

… operator ring (Ore extension) R[6;d~]. In this paper we compute the Krull dimension of R[9;d~] …
dimension then the Krull and global dimensions agree. We also prove some results on the …

… modules with Krull-dimensionover a polynomial ring and also study the case of group rings.
It has been pointed out to me that M. Teply has proved that V-rings with Krull dimension are …