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It is shown that a ring $R$ is a $G M$ -ring if and only if there exists a complete orthogonal set ${e_{1}, \dots, e_{n}}$ of idempotents such that all $e_{i} R e_{i}$ are $G M$ -rings. We also investigate $G M$ -rings for Morita contexts, module extensions and power series rings.

Extensions of hereditary algebras.

Nikolaos Marmaridis (1984)

Manuscripta mathematica

Extensions of nilpotent blocks.

Lluis Puig, Burkhard Külshammer (1990)

Inventiones mathematicae

Extensions of rational modules.

Cuadra, J. (2003)

International Journal of Mathematics and Mathematical Sciences

Extensions of semimodules and the Takahashi functor ${Ext}_{Λ} (C, A)$ .

Patchkoria, Alex (2003)

Homology, Homotopy and Applications

Extremal properties for concealed-canonical algebras

Michael Barot, Dirk Kussin, Helmut Lenzing (2013)

Colloquium Mathematicae

Canonical algebras, introduced by C. M. Ringel in 1984, play an important role in the representation theory of finite-dimensional algebras. They also feature in many other mathematical areas like function theory, 3-manifolds, singularity theory, commutative algebra, algebraic geometry and mathematical physics. We show that canonical algebras are characterized by a number of interesting extremal properties (among concealed-canonical algebras, that is, the endomorphism rings of tilting bundles on...

Extreme preservers of maximal column rank inequalities of matrix sums over semirings

Seok-Zun Song, Kwon-Ryong Park (2008)

Czechoslovak Mathematical Journal

We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings.

$f$ -derivations on rings and modules

Paul E. Bland (2006)

Commentationes Mathematicae Universitatis Carolinae

If $τ$ is a hereditary torsion theory on ${𝐌𝐨𝐝}_{R}$ and $Q_{τ} : {𝐌𝐨𝐝}_{R} \to {𝐌𝐨𝐝}_{R}$ is the localization functor, then we show that every $f$ -derivation $d : M \to N$ has a unique extension to an $f_{τ}$ -derivation $d_{τ} : Q_{τ} (M) \to Q_{τ} (N)$ when $τ$ is a differential torsion theory on ${𝐌𝐨𝐝}_{R}$ . Dually, it is shown that if $τ$ is cohereditary and $C_{τ} : {𝐌𝐨𝐝}_{R} \to {𝐌𝐨𝐝}_{R}$ is the colocalization functor, then every $f$ -derivation $d : M \to N$ can be lifted uniquely to an $f_{τ}$ -derivation $d_{τ} : C_{τ} (M) \to C_{τ} (N)$ .

$f$ -radical extensions of rings

Jeffrey Bergen, Antonio Giambruno (1987)

Rendiconti del Seminario Matematico della Università di Padova

Factors of Wild, Concealed Algebras.

Dieter Happel, Luise Unger (1989)

Mathematische Zeitschrift

Fair-sized projective modules

Pavel Příhoda (2010)

Rendiconti del Seminario Matematico della Università di Padova

Faithful linear representations of bands.

F. Cedó, J. Okninski (2009)

Publicacions Matemàtiques

Faithfully quadratic rings - a summary of results

M. Dickmann, F. Miraglia (2016)

Banach Center Publications

This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math. Soc. 2015), presented by the first author at the ALANT conference, Będlewo, Poland, June 8-13, 2014. The notions involved and the results are stated in detail, the techniques employed briefly outlined, but proofs are omitted. We focus on those aspects of the cited monograph concerning (diagonal) quadratic forms over preordered rings.

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