Moduli uniseriali non standard

Vengono esposti i risutati ottenuti per i moduli uniseriali non standard su domini di valutazione, a partire dalla prima dimostrazione della loro esistenza, data da Shelah nel 1984: le altre prove di esistenza, la loro struttura interna, l'organizzazione in una certa gerarchia ed alcune applicazioni, tra cui la soluzione di un problema posto da Kaplansky ed una generalizzazione della classica equivalenza di Matlis. The results obtained for non standard uniserial modules over valuation domains after the first proof of their existence given by Shelah in 1984 are exposed: the other existence proofs, their internal structure, the organization of their class in a suitable hierarchy, and some applications, as the solution of a problem posed by Kaplansky and a generalization of the classical equivalence.

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(Conferenza tenuta il 20 maggio 1990)     

I λ-Groups and almost totally injective groups

Summary We introduce the class ofI _λ-groups, where λ is an ordinal, consisting of these abelianp-groupsG such thatG/p ^σ G is almost totally injective for every ordinal σ<λ. As an application of some results onI _λ-groups, we prove an extension property of almost totally injective groups.

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Riassunto Si introduce la classe degliI _λ-gruppi, dove λ è un ordinale, formata daip-gruppi abelianiG tali cheG/p ^σ G è quasi totalmente iniettivo per ogni ordinale σ<λ. Come applicazione di alcuni risultati sugliI _λ-gruppi, si prova una proprietà di estensione dei gruppi quasi totalmente iniettivi.

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Lavoro eseguito nell'ambito dei Gruppi di Ricerca Matematica del Consiglio Nazionale delle Ricerche.     

Kinetic and mechanistic study of the gas-phase reactions of a series of vinyl ethers with the nitrate radical

NO(3) oxidation of methyl, ethyl, propyl, and butyl vinyl ethers has been studied under tropospheric conditions (atmospheric pressure and T = 293 +/- 3 K) in the LISA indoor simulation chamber. NO(3) was produced inside the reactor by thermal decomposition of N(2)O(5) previously added to the air-VOC mixture, and concentrations were monitored using FTIR spectrometry. All the kinetic experiments were carried out by relative rate technique using isoprene as reference compound, leading to the rate constants k(1) = (7.2 +/- 1.5) x 10(-13), k(2) = (13.1 +/- 2.7) x 10(-13), k(3) = (13.3 +/- 3.0) x 10(-13), and k(4) = (17.0 +/- 3.7) x 10(-13) cm(3) molecule(-1) s(-1) for methyl, ethyl, propyl, and butyl vinyl ethers, respectively. Main oxidation products have been identified like being formaldehyde and respectively methyl, ethyl, propyl, and butyl formates. Production yields of oxidation products were close to 50%. Oxygenated nitrates and peroxynitrates were also detected.     

Almost perfect commutative rings

Almost perfect commutative rings R are introduced (as an analogue of Bazzoni and Salce's almost perfect domains) for rings with divisors of zero: they are defined as orders in commutative perfect rings such that the factor rings $R/Rr$ are perfect rings (in the sense of Bass) for all non-zero-divisors$r\in R$. It is shown that an almost perfect ring is an extension of a T-nilpotent ideal by a subdirect product of a finite number of almost perfect domains. Noetherian almost perfect rings are exactly the one-dimensional Cohen–Macaulay rings. Several characterizations of almost perfect domains carry over practically without change to almost perfect rings. Examples of almost perfect rings with zero-divisors are abundant.     

Ion channeling studies of KTaO3:Nb

Ion channeling measurements have been performed on KTaO₃:Nb (KTN) in order to check the position of Nb relative to the tantalum site. No evidence for “off-center” Nb was found in the limit of experimental accuracy. In addition, the carbon content of the samples was measured and large concentrations were found (?300 p.p.m. weight). Possible relationship between Nb location and carbon presence is discussed.     

Uniserial modules: sums and isomorphisms of subquotients

Let R be an associative ring with 1. A left R module M is uniserial i f the lattice L(M) of its submodules is totally ordered under inclusion. We give an example of a uniserial module M with the property of having two submodules 0 < H < K < M such that M is isomorphic to K/H (we call a module M with this property shrinkable). Then we give an example of a uniserial module M isomorphic to all its nonzero quotients M/N, N<M, and with L(M) isomorphic to ω²+1; this solves a problem of Hirano and Mogami [7]. Finally we show that for uniserial modules the property of being shrinkable is connected to the problem of deciding whether a module, which is both a homomorphic image of a finite direct sum of uniserial modules and a submodule of a finite direct sum of uniserial modules, is a finite direct sum of uniserial modules     

Fully inert subgroups of free Abelian groups

A subgroup \(H\) of an Abelian group \(G\) is called fully inert if \((\phi H + H)/H\) is finite for every \(\phi \in \mathrm{End}(G)\) . Fully inert subgroups of free Abelian groups are characterized. It is proved that \(H\) is fully inert in the free group \(G\) if and only if it is commensurable with \(n G\) for some \(n \ge 0\) , that is, \((H + nG)/H\) and \((H + nG)/nG\) are both finite. From this fact we derive a more structural characterization of fully inert subgroups \(H\) of free groups \(G\) , in terms of the Ulm–Kaplansky invariants of \(G/H\) and the Hill–Megibben invariants of the exact sequence \(0 \rightarrow H \rightarrow G \rightarrow G/H \rightarrow 0\) .