Explicitly Non-Standard Uniserial Modules
نویسنده
چکیده
A new construction is given of non-standard uniserial modules over certain valuation domains; the construction resembles that of a special Aronszajn tree in set theory. A consequence is the proof of a sufficient condition for the existence of non-standard uniserial modules; this is a theorem of ZFC which complements an earlier independence result.
منابع مشابه
Almost uniserial modules
An R-module M is called Almost uniserial module, if any two non-isomorphic submodules of M are linearly ordered by inclusion. In this paper, we investigate some properties of Almost uniserial modules. We show that every finitely generated Almost uniserial module over a Noetherian ring, is torsion or torsionfree. Also the construction of a torsion Almost uniserial modules whose first nonzero Fit...
متن کاملOn the Noetherian dimension of Artinian modules with homogeneous uniserial dimension
In this article, we first show that non-Noetherian Artinian uniserial modules over commutative rings, duo rings, finite $R$-algebras and right Noetherian rings are $1$-atomic exactly like $Bbb Z_{p^{infty}}$. Consequently, we show that if $R$ is a right duo (or, a right Noetherian) ring, then the Noetherian dimension of an Artinian module with homogeneous uniserial dim...
متن کاملOn a non-vanishing Ext
The existence of valuation domains admitting non-standard uniserial modules for which certain Exts do not vanish was proved in [1] under Jensen’s Diamond Principle. In this note, the same is verified using the ZFC axioms alone. In the construction of large indecomposable divisible modules over certain valuation domainsR, the first author used the property thatR satisfied Ext1R(Q,U) 6= 0, where ...
متن کاملOn a Conjecture regarding Non-standard Uniserial Modules
We consider the question of which valuation domains (of cardinality א1) have nonstandard uniserial modules. We show that a criterion conjectured by Osofsky is independent of ZFC + GCH. 1991 Mathematics Subject Classification. Primary 13L05, 03E35, 13C05; Secondary 03E75, 13A18.
متن کاملSOME REMARKS ON ALMOST UNISERIAL RINGS AND MODULES
In this paper we study almost uniserial rings and modules. An R−module M is called almost uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is an almost left uniserial ring if R_R is almost uniserial. We give some necessary and sufficient condition for an Artinian ring to be almost left uniserial.
متن کامل