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Search: All articles in the CMB digital archive with keyword amalgamation

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1. CMB 2011 (vol 56 pp. 564)

Herzog, Ivo
Ziegler's Indecomposability Criterion
Ziegler's Indecomposability Criterion is used to prove that a totally transcendental, i.e., $\Sigma$-pure injective, indecomposable left module over a left noetherian ring is a directed union of finitely generated indecomposable modules. The same criterion is also used to give a sufficient condition for a pure injective indecomposable module ${_R}U$ to have an indecomposable local dual $U_R^{\sharp}.$

Keywords:pure injective indecomposable module, local dual, generic module, amalgamation
Categories:16G10, 03C60

2. CMB 2009 (vol 52 pp. 273)

MacDonald, John; Scull, Laura
Amalgamations of Categories
We consider the pushout of embedding functors in $\Cat$, the category of small categories. We show that if the embedding functors satisfy a 3-for-2 property, then the induced functors to the pushout category are also embeddings. The result follows from the connectedness of certain associated slice categories. The condition is motivated by a similar result for maps of semigroups. We show that our theorem can be applied to groupoids and to inclusions of full subcategories. We also give an example to show that the theorem does not hold when the property only holds for one of the inclusion functors, or when it is weakened to a one-sided condition.

Keywords:category, pushout, amalgamation
Categories:18A30, 18B40, 20L17

3. CMB 2003 (vol 46 pp. 122)

Moon, Myoungho
On Certain Finitely Generated Subgroups of Groups Which Split
Define a group $G$ to be in the class $\mathcal{S}$ if for any finitely generated subgroup $K$ of $G$ having the property that there is a positive integer $n$ such that $g^n \in K$ for all $g\in G$, $K$ has finite index in $G$. We show that a free product with amalgamation $A*_C B$ and an $\HNN$ group $A *_C$ belong to $\mathcal{S}$, if $C$ is in $\mathcal{S}$ and every subgroup of $C$ is finitely generated.

Keywords:free product with amalgamation, $\HNN$ group, graph of groups, fundamental group
Categories:20E06, 20E08, 57M07

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