منابع مشابه
Covers, Preenvelopes, and Purity
We show that if a class of modules is closed under pure quotients, then it is precovering if and only if it is covering, and this happens if and only if it is closed under direct sums. This is inspired by a dual result by Rada and Saorín. We also show that if a class of modules contains the ground ring and is closed under extensions, direct sums, pure submodules, and pure quotients, then it for...
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Adámek and Sousa recently solved the problem of characterizing the subcategories K of a locally λ-presentable category C which are λ-orthogonal in C, using their concept of Kλ-pure morphism. We strenghten the latter definition, in order to obtain a characterization of the classes defined by orthogonality with respect to λ-presentable morphisms (where f :A B is called λ-presentable if it is a λ-...
متن کاملLogical and Semantic Purity
Many mathematicians have sought ‘pure’ proofs of theorems. There are different takes on what a ‘pure’ proof is, though, and it’s important to be clear on their differences, because they can easily be conflated. In this paper I want to distinguish between two of them. I want to begin with a classical formulation of purity, due to Hilbert: In modern mathematics one strives to preserve the purity ...
متن کاملObservational Purity and Encapsulation
Practical specification languages for imperative and object-oriented programs, such as JML, Eiffel, and Spec#, allow the use of program expressions including method calls in specification formulas. For coherent semantics of specifications, and to avoid anomalies with runtime assertion checking, expressions in specifications and assertions are typically required to be weakly pure in the sense th...
متن کاملPurity and Gorenstein Filtered Rings
In this paper, we discuss on the existence of filtrations of modules having good properties. In particular, we focus on filtered homomorphisms called strict, and show that there exists a filtration which makes a filtered homomorphism a strict filtered homomorphism. Moreover, by using this result, we study purity for filtered modules over a Gorenstein filtered ring.
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ژورنال
عنوان ژورنال: CrossCurrents
سال: 2019
ISSN: 0011-1953,1939-3881
DOI: 10.1111/cros.12377