Similarity Classes of 3 × 3 Matrices Over a Local Principal Ideal Ring

Similarity Classes of 3× 3 Matrices over a Local Principal Ideal Ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.

Mutation Classes of Skew-symmetrizable 3× 3 Matrices

Mutation of skew-symmetrizable matrices is a fundamental operation that first arose in Fomin-Zelevinsky’s theory of cluster algebras; it also appears naturally in many different areas of mathematics. In this paper, we study mutation classes of skew-symmetrizable 3 × 3 matrices and associated graphs. We determine representatives for these classes using a natural minimality condition, generalizin...

A pr 2 00 7 The Invariant Ring of Triples of 3 × 3 Matrices over a Field of Arbitrary Characteristic

Let Rn,d be the ring of invariants of d-tuples of n × n matrices under the simultaneous conjugation action of the general linear group. A minimal generating system and a homogeneous system of parameters of R3,3 are determined. Homogeneous systems of parameters of R3,2, R4,2 are also pointed out.

Classification based on 3-similarity

Similarity concept, finding the resemblance or classifying some groups of objects and study their common properties has been the interest of many researchers. Basically, in the studies the similarity between two objects or phenomena, 2-similarity in our words, has been discussed. In this paper, we consider the case when the resemblance or similarity among three objects or phenomena of a set, 3-...

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring