A characterization of subgroup lattices of finite abelian groups.
A characterization of the Artinian modules.
A Class of Balanced Non-Uniserial Rings.
A criterion for quasi-heredity and the characteristic module.
A duality result for almost split sequences
Over an artinian hereditary ring R, we discuss how the existence of almost split sequences starting at the indecomposable non-injective preprojective right R-modules is related to the existence of almost split sequences ending at the indecomposable non-projective preinjective left R-modules. This answers a question raised by Simson in [27] in connection with pure semisimple rings.
A Krull-Schmidt theorem for Artinian modules over local rings.
A note on hereditary rings or non-singular rings with chain condition.
A representation theorem for Chain rings
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.
Addendum to “Ring elements as sums of units”
We give a comment to Theorem 1.1 published in our paper “Ring elements as sums of units” [Cent. Eur. J. Math., 2009, 7(3), 395–399].
An Application of a Theorem of Ziegler.
Anneaux semi-artiniens
Artinische Ringe mit artinischem Radikal.