Injective and automorphism-invariant non-singular modules

Tuganbaev, A. A.

doi:10.1080/00927872.2017.1354011

Cited by 5 publications

(1 citation statement)

References 19 publications

(16 reference statements)

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“…Модуль, инвариантный относительно автоморфизмов своей инъективной оболочки, называется автоморфизминвариантным. Автоморфизм-инвариантные модули впервые рассмотрены Диксоном и Фуллером в [1] и в последнее время систематически изучены в [2][3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionunclassified

Кольца, У Которых Каждый Правый Идеал Является Конечной Прямой Суммой Автоморфизм-Инвариантных Правых Идеалов

Abyzov¹,

Phan²,

Truong³

2020

Sib. Mat. Zh.

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Section: Introductionunclassified

Кольца, У Которых Каждый Правый Идеал Является Конечной Прямой Суммой Автоморфизм-Инвариантных Правых Идеалов

Abyzov¹,

Phan²,

Truong³

2020

Sib. Mat. Zh.

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Invariance of Modules under Automorphisms of their Envelopes and Covers

Srivastava

Tuganbaev

Asensio

2021

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The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.

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Rings Whose Every Right Ideal is a Finite Direct Sum of Automorphism-Invariant Right Ideals

2020

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Injective and automorphism-invariant non-singular modules

Abstract: Abstract. Every automorphism-invariant right non-singular A-module is injective if and only if the factor ring of the ring A with respect to its right Goldie radical is a right strongly semiprime ring.The study is supported by Russian Scientific Foundation (project 16-11-10013).

Cited by 5 publications

References 19 publications

Кольца, У Которых Каждый Правый Идеал Является Конечной Прямой Суммой Автоморфизм-Инвариантных Правых Идеалов

Кольца, У Которых Каждый Правый Идеал Является Конечной Прямой Суммой Автоморфизм-Инвариантных Правых Идеалов

Invariance of Modules under Automorphisms of their Envelopes and Covers

Rings Whose Every Right Ideal is a Finite Direct Sum of Automorphism-Invariant Right Ideals

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