Injective Envelopes and Projective Covers of Quivers
نویسنده
چکیده
This paper characterizes the injective and projective objects in the category of directed multigraphs, or quivers. Further, the injective envelope and projective cover of any quiver in this category is constructed.
منابع مشابه
Flat Covers of Representations of the Quiver
Rooted quivers are quivers that do not contain A∞ ≡ ··· → • → • as a subquiver. The existence of flat covers and cotorsion envelopes for representations of these quivers have been studied by Enochs et al. The main goal of this paper is to prove that flat covers and cotorsion envelopes exist for representations of A∞. We first characterize finitely generated projective representations of A∞. We ...
متن کاملar X iv : m at h / 07 02 79 3 v 1 [ m at h . R A ] 2 6 Fe b 20 07 INJECTIVE REPRESENTATIONS OF INFINITE QUIVERS . APPLICATIONS
In this article we study injective representations of infinite quivers. We classify the indecomposable injective representations of trees and then describe Gorenstein injective and projective representations of barren trees.
متن کامل$mathcal{X}$-injective and $mathcal{X}$-projective complexes
Let $mathcal{X}$ be a class of $R$-modules. In this paper, we investigate ;$mathcal{X}$-injective (projective) and DG-$mathcal{X}$-injective (projective) complexes which are generalizations of injective (projective) and DG-injective (projective) complexes. We prove that some known results can be extended to the class of ;$mathcal{X}$-injective (projective) and DG-$mathcal{X}$-injective ...
متن کاملA Note on the Radical of a Module Category
We characterize the finiteness of the representation type of an artin algebra in terms of the behavior of the projective covers and the injective envelopes of the simple modules with respect to the infinite radical of the module category. In case the algebra is representation-finite, we show that the nilpotency of the radical of the module category is the maximal depth of the composites of thes...
متن کاملEssential Weak Factorization Systems
We discuss a new type of weak factorization system. Although these systems provide (up to isomorphism) uniquely determined decompositions of morphisms, in general they do not constitute orthogonal factorizations and are not even functorial. Nevertheless, they arise naturally, as injective hulls or projective covers in comma categories. Surprisingly, often injective hulls and projective covers c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012