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We describe all those indecomposable primarily comultiplication modules with finite-dimensional top over pullback of two Dedekind domains. We extend the definition and results given by R. Ebrahimi Atani and S. Ebrahimi Atani [Algebra Discrete Math. 2009] to a more general primarily comultiplication modules case.

Indecomposable projective modules on affine domains

V. Srinivas (1986)

Compositio Mathematica

Independence in Completions and Endomorphism Algebras.

Rüdiger Göbel, Warren May (1989)

Forum mathematicum

Injective and projective properties of $R [x]$ -modules

Sangwon Park, Eunha Cho (2004)

Czechoslovak Mathematical Journal

We study whether the projective and injective properties of left $R$ -modules can be implied to the special kind of left $R [x]$ -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.

Injective Moduls over Krull Orders.

Robert Fossum (1971)

Mathematica Scandinavica

Intermediate domains between a domain and some intersection of its localizations

Mabrouk Ben Nasr, Noômen Jarboui (2002)

Bollettino dell'Unione Matematica Italiana

In this paper, we deal with the study of intermediate domains between a domain $R$ and a domain $T$ such that $T$ is an intersection of localizations of $R$ , namely the pair $(R, T)$ . More precisely, we study the pair $(R, R_{d})$ and the pair $(R, \tilde{R})$ , where $R_{d} = \cap \{R_{M} ∣ M \in Max (R), h t M = dim R\}$ and $\tilde{R} = \cap \{R_{M} ∣ M \in Max (R), h t M \geq 2\}$ . We prove that, if $R$ is a Jaffard domain, then $(R, R_{d} [n])$ is a Jaffard pair, which generalize [5, Théorème 1.9]. We also show that if $R$ is an $S$ -domain, then $(R, \tilde{R})$ is a residually algebraic pair (that is for each intermediate domain $S$ between $R$ and $\tilde{R}$ , if $Q$ is a prime ideal of $S$ ...

Invariante Untermoduln quadratischer Moduln.

M. Kneser, U. Stuhler, A. Kallmann (1973)

Journal für die reine und angewandte Mathematik

Invarianten wesentlicher Überdeckungen.

Helmut Zöschinger (1978)

Mathematische Annalen

Invariants for quasi-injective modules over valuation domains

Luigi Salce (2016)

Colloquium Mathematicae

Quasi-injective modules over valuation domains are classified by means of complete sets of cardinal invariants.

Inversion of Monic polynomials and Existence of Unimodular Elements (II).

S.M. Bhatwadekar (1988/1989)

Mathematische Zeitschrift

Inversion of Monic Polynomials and Existence of Unimodular Elements.

Amit Roy, Shrikant M. Bhatwadekar (1983)

Mathematische Zeitschrift

Isolated points and redundancy

P. Alirio J. Peña, Jorge E. Vielma (2011)

Commentationes Mathematicae Universitatis Carolinae

We describe the isolated points of an arbitrary topological space $(X, τ)$ . If the $τ$ -specialization pre-order on $X$ has enough maximal elements, then a point $x \in X$ is an isolated point in $(X, τ)$ if and only if $x$ is both an isolated point in the subspaces of $τ$ -kerneled points of $X$ and in the $τ$ -closure of ${x}$ (a special case of this result is proved in Mehrvarz A.A., Samei K., On commutative Gelfand rings, J. Sci. Islam. Repub. Iran 10 (1999), no. 3, 193–196). This result is applied to an arbitrary subspace of the prime...

Isomorphism of Endomorphism Algebras over Complete Discrete Valuation Rings.

Warren May (1990)

Mathematische Zeitschrift

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