Results 1 to 10 of about 3,139 (196)
Projective and injective modules [PDF]
Archiv der Mathematik, 1960 For a ring A, the following conditions are equivalent. (1) All right A-modules are free. (2) There exists a simple free module MA. (3) AA is a simple module. (4) All nonzero elements of A are right mvertible. (5) A is a division ring.
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On projective and injective polynomial modules [PDF]
Mathematische Zeitschrift, 2005 Let \(k\) be a field and \(n\geq 0\). One has a category \(\text{Pol}(n)\) of polynomial representations of the general linear group \(\text{GL}_n\) over \(k\). The authors look for the indecomposable injectives in this category that are at the same time projective. Let \(I(\lambda)\) denote the injective whose socle has highest weight \(\lambda\). If \
De Visscher, M., Donkin, S.
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Injectivity and projectivity in analysis and topology [PDF]
Science China Mathematics, 2011 We give new proofs for many injectivity results in analysis that make more careful use of the duality between unital abelian C*-algebras and compact Hausdorff spaces. We then extend many of these results to incorporate group actions. Our approach uses only elementary topological constructions and eliminates the need for results from the theory of ...
Hadwin, Don, Paulsen, Vern I.
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Conductor, projectivity and injectivity [PDF]
Pacific Journal of Mathematics, 1973 This paper discusses the rôle of the conductor of a ring extension vis-à-vis the descent of projectivity and injectivity. Regarding the former, the first result says that an injective homomorphism of commutative rings descends the projectivity if it does so modulo the conductor.
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About the Normal Projectivity and Injectivity of Krasner Hypermodules [PDF]
Axioms, 2021 Inspired by the concepts of projective and injective modules in classical algebraic structure theory, in this paper we initiate the study of the chains of hypermodules over a Krasner hyperring R, endowing first the set HomRn(M,N) of all normal homomorphisms between two R-hypermodules M and N with a structure of R-hypermodule. Then, our study focuses on
Hashem Bordbar, Irina Cristea
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The Injective and Projective Leavitt Complexes [PDF]
, 2020 arXiv admin note: text overlap with arXiv:1512.04178, arXiv:1610.00144; text overlap with arXiv:1301.0195 by other ...
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C-Gorenstein projective, injective and flat modules [PDF]
Czechoslovak Mathematical Journal, 2009 In this paper, we study some properties of Ω-Gorenstein projective, injective and flat modules and discuss some connections between Ω-Gorenstein injective and Ω-Gorenstein flat modules. We also consider these properties under change of rings.
Yang, Xiaoyan, Liu, Zhongkui
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Injective Envelopes and Projective Covers of Quivers [PDF]
The Electronic Journal of Combinatorics, 2012 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.
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Journal of Algebra, 1993 By \(R\) is denoted a semiprimary ring with identity 1 and \(R\)-modules be unitary. For a left \(R\)-module \(M\) the injective hull of \(M\) is denoted by \(E(M)\), the socle of \(M\) by \(S(M)\), the Jacobson radical by \(\text{rad}(M)\) and the top \(M/(\text{rad}(M))\) by \(T(M)\).
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Injectivity and projectivity in p-multinormed spaces [PDF]
Positivity, 2018 We find large classes of injective and projective $p$-multinormed spaces. In fact, these classes are universal, in the sense that every $p$-multinormed space embeds into (is a quotient of) an injective (resp. projective) $p$-multinormed space. As a consequence, we show that any $p$-multinormed space has a canonical representation as a subspace of a ...
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