Results 131 to 140 of about 39,390 (167)
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1974
For each ring R we have derived several module categories—among these the category R M of left R-modules. This derivation is not entirely reversible for, in general, R M does not characterize R. However, as we shall see in Chapter 6 it does come close. Thus, we can expect to uncover substantial information about R by mining R M.
Frank W. Anderson, Kent R. Fuller
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For each ring R we have derived several module categories—among these the category R M of left R-modules. This derivation is not entirely reversible for, in general, R M does not characterize R. However, as we shall see in Chapter 6 it does come close. Thus, we can expect to uncover substantial information about R by mining R M.
Frank W. Anderson, Kent R. Fuller
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Summing up and future directions
1996Abstract The ability to move is one of the most important characteristics of living things. Migration in all its often astonishing variety is the most elaborate expression of that ability, and its prevalence in so great a diversity of organisms demonstrates that it has been repeatedly favored by natural selection over alternative ...
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2002
If A and B are non-empty subsets of a vector space V over a field F then the subspace spanned by A ∪ B, i.e. the smallest subspace of V that contains both A and B, is the set of linear combinations of elements of A ∪ B. In other words, it is the set of elements of the form $$ [\sum\limits_{i = 1}^m {{\lambda _i}} {a_i} + \sum\limits_{j = 1}^n {{\mu
T. S. Blyth, E. F. Robertson
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If A and B are non-empty subsets of a vector space V over a field F then the subspace spanned by A ∪ B, i.e. the smallest subspace of V that contains both A and B, is the set of linear combinations of elements of A ∪ B. In other words, it is the set of elements of the form $$ [\sum\limits_{i = 1}^m {{\lambda _i}} {a_i} + \sum\limits_{j = 1}^n {{\mu
T. S. Blyth, E. F. Robertson
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Infinite Direct Sums of Lifting Modules
Communications in Algebra, 2006A module M over a ring R is called a lifting module if every submodule A of M contains a direct summand K of M such that A/K is a small submodule of M/K (e.g., local modules are lifting). It is known that a (finite) direct sum of lifting modules need not be lifting.
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Perturbation of Direct Sum Differential Operators
Canadian Journal of Mathematics, 1978Let I be an interval, and let for 1 ≦ j ≦ I < ∞ be abutted subintervals such that . Let τ j be a linear differential expression defined on I j . In this paper we study densely defined operators associated with
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DIRECT SUMS OF H-SUPPLEMENTED MODULES
Journal of Algebra and Its Applications, 2013A module M is said to be H-supplemented if, for any submodule X of M, there exists a direct summand M′ of M such that M = X + Y if and only if M = M′ + Y for all Y ⊆ M (cf. [S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Mathematical Society Lecture Note Series, Vol. 147 (Cambridge University Press, 1999)]).
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Direct Sums of Torsion-Free Covers
Canadian Journal of Mathematics, 1973In [4, Theorem 4.1, p. 45], Enochs characterizes the integral domains with the property that the direct product of any family of torsion-free covers is a torsion-free cover. In a setting which includes integral domains as a special case, we consider the corresponding question for direct sums. We use the notion of torsion introduced by Goldie [5]. Among
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Factor categories and infinite direct sums
2009We give an improved categorical version of the Weak Krull-Schmidt Theorem for serial modules proved by the second author in [10]. The main improvement consists in the fact that it applies not only to serial modules, but also, more generally, to arbitrary direct summands of serial modules.
FACCHINI, ALBERTO, PRIHODA P.
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