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1
Foundations of Module and Ring Theory
Uniserial modules. 2. Serial modules. 3. Left serial rings. 4. Relations with -i\M). S
.Exchange property, t). Serial modules with extension property. 7. When are nil
finitely M-presented modules serial? 8.Serial rings. g. Modules with uniserial ...
2
Representation Theory of Artin Algebras
Lemma 2.5 Let A be an artin algebra which is a sum of uniserial modules. Then
the following are equivalent for a A-module C. (a) C/rC is simple. (b) If P — » C is
a projective cover, then P is uniserial. (c) C is uniserial. Moreover, if A and B are ...
3
A First Course in Noncommutative Rings
We have mentioned in this section that End(MR) is a semilocal ring if M R is an
artinian module (result of Camps-Dicks) or a uniserial module (result of Facchini)
over any ring R. These results provide new interesting classes of semilocal rings,
...
4
Module Theory: Endomorphism rings and direct sum ...
and. modules. Recall that an R-module M is said to be uniserial if for any
submodules A and B of M we have A Q B or B Q A. Hence a module M is
uniserial if and only if the lattice C(M) of its submodules is linearly ordered under
set inclusion.
5
Advances in Algebra and Model Theory
existence of a faithful uniserial fi-module U does imply, in some relevant cases,
that either R is a valuation ring, or a suitable ring obtained by R and determined
by U (over which U is canonically a uniserial module) is a valuation ring. In fact, if
...
6
Algebras, Rings and Modules: Volume 1
This result was generalized by T.Nakayama for Artinian serial rings, who called
these rings ”generalized uniserial rings”, (see T.Nakayama, On Frobeniusean
algebras I,II // Ann. of Math., v.40 (1939), p.611633; v.42(1941), p.1-21 and Note
on ...
Michiel Hazewinkel, Nadezhda Mikhaĭlovna Gubareni, Vladimir V. Kirichenko, 2006
7
Modules Over Non-Noetherian Domains
Chapter X Uniserial Modules The primary aim in this chapter is to give a general
development of uniserial modules. These modules form a class whose
significance is due to their role in the study of modules over valuation domains;
as a ...
László Fuchs, Luigi Salce, 2001
8
Purity, Spectra and Localisation
The endomorphism ring of a uniserial module need not be local: there is a
counterexample over a ring of Krull dimension 1 at [183, 9.26].11 If, however, the
ring is commutative or right noetherian, then the endomorphism ring of a uniserial
...
9
Canadian Journal of Mathematics
property. Conversely, if R/J- has every indecomposable injective left R- module
uniserial, then so does R. Proof. Let R/I be a factor ring of R and £R// be an
indecomposable injective over R/I. As S(ER/i) is simple, the injective hull of ERII
is ...
10
The Jacobson Radical of Group Algebras
G. Karpilovsky. k-1 k-i J(A) V = J(A) 'M5 >lJ(A)i+lV k _lJ(A)7'.V = J(A) = J(A) V = 0,
a contradiction. The conclusion is that, if k is the Loewy length of V, then V 3 J(A)
V 3 J(A)2V 3 ... 3 J%A)k_lV 3 O The module V is said to be uniserial if the above ...
WIADOMOŚCI, KTÓRE ZAWIERAJĄ SŁOWO «UNISERIAL»
Sprawdź, o czym dyskutuje się w prasie krajowej i zagranicznej oraz jak jest stosowane słowo
uniserial w wiadomościach.
The man who was jailed for 22 years – on the fantasy evidence of a …
Its text is peppered with scientific language – sebaceous gland, papilla, uniserial, vacuolated, cortex, cuticle. The assumption running through its 53 pages is that ... «The Guardian, Cze 15»
