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We first propose a generalization of the notion of Mathieu subspaces of associative algebras $𝒜$ , which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to $𝒜$ -modules $ℳ$ . The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable...

A non-commutative minimally non-Noetherian ring.

Jutta Hausen, Johnny A. Johson (1975)

Mathematica Scandinavica

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.

Addendum to “Ring elements as sums of units”

Charles Lanski, Attila Maróti (2013)

Open Mathematics

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].

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A characterization of representation-finite biserial algebras over a perfect field [Book]

A Class of Balanced Non-Uniserial Rings.

A combinatorial class number formula.

A commutativity-or-finiteness condition for rings.

A comparison of deformations and geometric study of varieties of associative algebras.

A construction for quasi-hereditary algebras

A Criterion for Finite Representation Type.

A generalization of Mathieu subspaces to modules of associative algebras

A non-commutative minimally non-Noetherian ring.

A representation theorem for Chain rings

Addendum to “Ring elements as sums of units”

Admissible groups, symmetric factor sets, and simple algebras.

Algebraically Compact Rings and Modules.

Algebras and Quaternion Defect Groups. I.

Algebras and Quaternion Defect Groups. II.

Algebras with Cycle-Finite Derived Categories.

Algebren, Darstellungsköcher, Ueberlagerungen und zurück.

Algèbres auto-injectives de représentation finie

Algèbres de type de représentation fini

Algunas observaciones acerca de matrices triangulares sobre anillos

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