Max-projective modules

Alagöz, Yusuf; Büyükaşık, Engı̇n

doi:10.1142/s021949882150095x

Cited by 3 publications

(1 citation statement)

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“…The category of modules is of special interest, in the general form (see, for example, [1,2]), or in special forms (see, for example, [3][4][5][6][7][8][9][10]).…”

Section: Introductionmentioning

confidence: 99%

On the Two Categories of Modules

Popescu

2022

Symmetry

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A new category equivalence is proved in this paper, involving the two distinct categories of modules, the covariant and the contravariant, respectively, released by Higgins and Mackenzie. The equivalence of the two categories is given when restricting to almost finitely generated projective modules and their allowed morphisms, defined in the paper. The equivalence is expressed by using generators. In particular, we obtain the well-known equivalence of the two categories of projective finitely generated modules; thus, our main result extends this classical one.

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“…The category of modules is of special interest, in the general form (see, for example, [1,2]), or in special forms (see, for example, [3][4][5][6][7][8][9][10]).…”

Section: Introductionmentioning

confidence: 99%

On the Two Categories of Modules

Popescu

2022

Symmetry

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Subprojectivity in Abelian Categories

Amzil

Bennis

Rozas

et al. 2021

Appl Categor Struct

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Some variations of projectivity

Ertaş

Tribak²

2021

J. Algebra Appl.

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We prove that a ring [Formula: see text] has a module [Formula: see text] whose domain of projectivity consists of only some injective modules if and only if [Formula: see text] is a right noetherian right [Formula: see text]-ring. Also, we consider modules which are projective relative only to a subclass of max modules. Such modules are called max-poor modules. In a recent paper Holston et al. showed that every ring has a p-poor module (that is a module whose projectivity domain consists precisely of the semisimple modules). So every ring has a max-poor module. The structure of all max-poor abelian groups is completely determined. Examples of rings having a max-poor module which is neither projective nor p-poor are provided. We prove that the class of max-poor [Formula: see text]-modules is closed under direct summands if and only if [Formula: see text] is a right Bass ring. A ring [Formula: see text] is said to have no right max-p-middle class if every right [Formula: see text]-module is either projective or max-poor. It is shown that if a commutative noetherian ring [Formula: see text] has no right max-p-middle class, then [Formula: see text] is the ring direct sum of a semisimple ring [Formula: see text] and a ring [Formula: see text] which is either zero or an artinian ring or a one-dimensional local noetherian integral domain such that the quotient field [Formula: see text] of [Formula: see text] has a proper [Formula: see text]-submodule which is not complete in its [Formula: see text]-topology. Then we show that a commutative noetherian hereditary ring [Formula: see text] has no right max-p-middle class if and only if [Formula: see text] is a semisimple ring.

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Max-projective modules

Cited by 3 publications

References 30 publications

On the Two Categories of Modules

On the Two Categories of Modules

Subprojectivity in Abelian Categories

Some variations of projectivity

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