Projective modules and approximation couples
Projective modules and prime submodules
In this paper, we use Zorn’s Lemma, multiplicatively closed subsets and saturated closed subsets for the following two topics: (i) The existence of prime submodules in some cases, (ii) The proof that submodules with a certain property satisfy the radical formula. We also give a partial characterization of a submodule of a projective module which satisfies the prime property.
Projective modules over real affine algebras.
Projective Resolutions of Cohen-Macaulay Algebras.
Projectivity of pure ideals
Rank of Submodule, Linear Transformations and Linearly Independent Subsets of Z-module
In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, and that there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts of linear transformations between two Z-modules. In this section, we define homomorphism between...
Remarks on faithful flatness
Remarks on reflexive modules, covers, and envelopes.
Résultats récents sur l'approximation des morphismes en algèbre commutative
Semisimple Algebras and a Cancellation Law.
Simple Flat Extensions. II.
Simple injective modules.
Small almost free modules with prescribed topological endomorphism rings
Some homological properties of amalgamated modules along an ideal
Let and be commutative rings with identity, be an ideal of , be a ring homomorphism, be an -module, be an -module, and let be an -homomorphism. The amalgamation of with along with respect to denoted by was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of -module called the amalgamation of and along with respect to , and denoted by . We study some homological properties of the -module . Among other results,...
Some morphisms of modules over the ring of pseudorational numbers.
Some remarks on Prüfer modules
We provide several characterizations and investigate properties of Prüfer modules. In fact, we study the connections of such modules with their endomorphism rings. We also prove that for any Prüfer module M, the forcing linearity number of M, fln(M), belongs to {0,1}.
Some Results about Modules over Discrete Hodge Algebras.
Some theorems on generation of ideals in affine algebras.
Stability, duality, 2-generated ideals and a canonical decomposition of modules
Stability Theorems for Overrings of Polynomial Rings.