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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 characterization of the Artinian modules.

Peña P., Alirio J. (1993)

Divulgaciones Matemáticas

A representation theorem for Chain rings

Yousef Alkhamees, Hanan Alolayan, Surjeet Singh (2003)

Colloquium Mathematicae

A ring A is called a chain ring if it is a local, both sided artinian, principal ideal ring. Let R be a commutative chain ring. Let A be a faithful R-algebra which is a chain ring such that Ā = A/J(A) is a separable field extension of R̅ = R/J(R). It follows from a recent result by Alkhamees and Singh that A has a commutative R-subalgebra R₀ which is a chain ring such that A = R₀ + J(A) and R₀ ∩ J(A) = J(R₀) = J(R)R₀. The structure of A in terms of a skew polynomial ring over R₀ is determined.

Abelian modules.

Agayev, N., Güngöroğlu, G., Harmanci, A., Halicioğlu, S. (2009)

Acta Mathematica Universitatis Comenianae. New Series

Addendum to "Rings whose modules have maximal submodules".

Carl Faith (1998)

Publicacions Matemàtiques

Addendum to the author's article "Rings whose modules have maximal submodules", which appeared in Publicacions Matemàtiques 39, 1 (1995), 201-214.

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