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A canonical directly infinite ring

Mario Petrich, Pedro V. Silva (2001)

Czechoslovak Mathematical Journal

Let $ℕ$ be the set of nonnegative integers and $ℤ$ the ring of integers. Let $ℬ$ be the ring of $N \times N$ matrices over $ℤ$ generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of $ℬ$ yields that the subrings generated by them coincide. This subring is the sum of the ideal $ℱ$ consisting of...

A family of noetherian rings with their finite length modules under control

Markus Schmidmeier (2002)

Czechoslovak Mathematical Journal

We investigate the category $mod Λ$ of finite length modules over the ring $Λ = A \otimes_{k} Σ$ , where $Σ$ is a V-ring, i.e. a ring for which every simple module is injective, $k$ a subfield of its centre and $A$ an elementary $k$ -algebra. Each simple module $E_{j}$ gives rise to a quasiprogenerator $P_{j} = A \otimes E_{j}$ . By a result of K. Fuller, $P_{j}$ induces a category equivalence from which we deduce that $mod Λ ≃ ∐_{j} b a d h b o x P_{j}$ . As a consequence we can (1) construct for each elementary $k$ -algebra $A$ over a finite field $k$ a nonartinian noetherian ring $Λ$ such that $mod A ≃ mod Λ$ , (2) find twisted...

Displaying 1 – 8 of 8

A canonical directly infinite ring

A family of noetherian rings with their finite length modules under control

A generalization of a theorem of Faith and Menal and applications.

A Note on Skew Polynomial Rings

A note on the simplicity of skew polynomial rings of derivation type

A Reduction Theorem for the Primitivity of Tensor Products.

A surjectivity theorem for rigid highest weight modules.

Automorphisms and f-simplicity in skew polynomial rings

Currently displaying 1 – 8 of 8