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⋂ -compact modules

Tomáš Kepka (1995)

Commentationes Mathematicae Universitatis Carolinae

The duals of ∪ -compact modules are briefly discussed.

( n , d ) -injective covers, n -coherent rings, and ( n , d ) -rings

Weiqing Li, Baiyu Ouyang (2014)

Czechoslovak Mathematical Journal

It is known that a ring R is left Noetherian if and only if every left R -module has an injective (pre)cover. We show that ( 1 ) if R is a right n -coherent ring, then every right R -module has an ( n , d ) -injective (pre)cover; ( 2 ) if R is a ring such that every ( n , 0 ) -injective right R -module is n -pure extending, and if every right R -module has an ( n , 0 ) -injective cover, then R is right n -coherent. As applications of these results, we give some characterizations of ( n , d ) -rings, von Neumann regular rings and semisimple rings....

ℵ-products of modules and splitness.

Feng Lianggui (2002)

Publicacions Matemàtiques

Let0 → ∏ℵI Mα ⎯λ→ ∏I Mα ⎯γ→ Coker λ → 0 be an exact sequence of modules, in which ℵ is an infinite cardinal, λ the natural injection and γ the natural surjection. In this paper, the conditions are given mainly in the four theorems so that λ (γ respectively) is split or locally split. Consequently, some known results are generalized. In particular, Theorem 1 of [7] and Theorem 1.6 of [5] are improved.

ω 1 -generated uniserial modules over chain rings

Jan Žemlička (2004)

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three two-sided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an ω 1 -generated uniserial module over every non-artinian nearly simple chain ring and over chain rings containing an uncountable strictly increasing (resp. decreasing)...

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