Some remarks on structural matrix rings and matrices with ideal entries

Some Remarks on Structural Matrix Rings and Matrices with Ideal Entries

Associating to each pre-order on the indices 1; :::;n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n n matrix rings. Rings within the order-convex hull of the embedding, i.e. matrix rings that contain the ring of diagonal matrices, can be viewed as incidence algebras of ideal-valued, generalized pre-order relation...

SOME REMARKS ON ALMOST UNISERIAL RINGS AND MODULES

In this paper we study almost uniserial rings and modules. An R−module M is called almost uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is an almost left uniserial ring if R_R is almost uniserial. We give some necessary and sufficient condition for an Artinian ring to be almost left uniserial.

Some Remarks on Affine Rings

Various topics on affine rings are considered, such as the relationship between Gelfand-Kirillov dimension and Krull dimension, and when a "locally affine" algebra is affine. The dimension result is applied to study prime ideals in fixed rings of finite groups, and in identity components of group-graded rings. 0. Introduction. We study affine rings (i.e., rings finitely generated as algebras ov...

Some Remarks on Fibonacci Matrices

In [1], Dazheng studies Fibonacci matrices, namely matrices M such that every entry of every positive power of M is either 0 or plus or minus a Fibonacci number. He gives 40 such four-byfour matrices. In the following, we give an interpretation of these matrices, from which we give simpler proofs of several of his theorems. We also determine all two-by-two Fibonacci matrices. Let £ = e be a pri...

Some Remarks on Elementary Divisor Rings II