Valuation derived from graded ring and module and Krull dimension properties

In this paper we show if R is a graded ring then we can dene avaluation on R induced by graded structure, and we prove some properties and relations for R. Later we show that if R is a graded ring and M a graded R-module then there exists a valuation on of M which is derived from graded structure and also we prove some properties and relations for R. In the following we give a new method for nding the Kurll dimension of a valuation ring.

Download Full-text

IS INFINITE DIMENSIONAL

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748020000201 ◽

2020 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Jaclyn Lang ◽

Judith Ludwig

Keyword(s):

Valuation Ring ◽

Krull Dimension ◽

Infinite Dimensional ◽

Witt Vectors

Given a perfect valuation ring $R$ of characteristic $p$ that is complete with respect to a rank- $1$ nondiscrete valuation, we show that the ring $\mathbb{A}_{\inf }$ of Witt vectors of $R$ has infinite Krull dimension.

Download Full-text

Selective Sampling and Orientation of Non-Homogeneous Tissues

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100100238 ◽

1968 ◽

Vol 26 ◽

pp. 98-99

Author(s):

C. C. Clawson ◽

L. W. Anderson ◽

R. A. Good

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Light Microscopy ◽

Random Sampling ◽

New Method ◽

Microscope Examination ◽

Small Areas ◽

Selective Sampling ◽

Large Numbers ◽

Specific Orientation

Investigations which require electron microscope examination of a few specific areas of non-homogeneous tissues make random sampling of small blocks an inefficient and unrewarding procedure. Therefore, several investigators have devised methods which allow obtaining sample blocks for electron microscopy from region of tissue previously identified by light microscopy of present here techniques which make possible: 1) sampling tissue for electron microscopy from selected areas previously identified by light microscopy of relatively large pieces of tissue; 2) dehydration and embedding large numbers of individually identified blocks while keeping each one separate; 3) a new method of maintaining specific orientation of blocks during embedding; 4) special light microscopic staining or fluorescent procedures and electron microscopy on immediately adjacent small areas of tissue.

Download Full-text