Closed Subcategories in Quotient Categories and Their Relationship to Filter Systems
This paper establishes a connection between closed subcategories in a Grothendieck category, particularly quotient categories, and specific filter systems within those categories, providing a framework for understanding their structure and relationships.
역방향 극한을 통한 정규 환 속성의 저하
역방향 극한 구조를 사용하면 단위 정칙성, 행렬의 대각화 가능성, 유한 안정 계수와 같은 정규 환의 속성이 저하될 수 있습니다.
Regular Ring Properties Degraded Through Inverse Limits: Exploring the Potential for Resolving the Separativity Problem
This paper explores the use of inverse limits in ring theory, demonstrating how this construction can lead to the degradation of desirable properties in regular rings, such as unit-regularity and finite stable rank, and discusses its potential application to the unresolved Separativity Problem.
Generalized Inverses and Their Relationship to Idempotent Endomorphisms (Projectors) in Rings
This paper explores the connection between generalized inverses in an associative ring and idempotent group endomorphisms, referred to as projectors, highlighting their role in characterizing and establishing existence conditions for various types of generalized inverses.
역반환 준환: 고리와 이뎀포텐트 준환을 넘어서는 대수적 구조
본 논문은 고리와 이뎀포텐트 준환을 일반화하는 역반환 준환의 개념, 속성, 중요성을 소개하고, 모듈, 아이디얼, E-단위 역반환 준군과의 관계 등 그 기본 이론을 탐구합니다.
The Theory of Inverse Semirings and Their Modules
This paper introduces inverse semirings, a generalization of both rings and idempotent semirings, and develops their basic theory, including the structure of their modules and ideals, highlighting connections to both ring theory and inverse semigroup theory.
Tilting Objects Induce Equivalences Between Q-Shaped Derived Categories and Ordinary Derived Categories
Under suitable hypotheses, there exists a triangulated equivalence between the Q-shaped derived category of an algebra A, denoted DQ(A), and the classic derived category D(B) of a different algebra B.
Rings Characterized by the Property that u^n-1 Belongs to the Subring Delta(R) for Every Unit u
The article explores the properties of n-∆U rings, a class of rings defined by the condition that for every unit element u in the ring, u^n - 1 belongs to a specific subring ∆(R).
준단순 좌측 골디 환의 단사 내형성사상에 대한 르로이-마츠척 질문에 대한 긍정적 답변
이 논문은 준단순 좌측 골디 환의 큰 이미지를 갖는 모든 내형성사상이 단사임을 증명하여 르로이-마츠척의 질문에 긍정적으로 답변합니다.
Injectivity of Endomorphisms of Semiprime Left Noetherian Rings with Large Images: An Affirmative Answer to Leroy and Matczuk's Question
Every endomorphism with a large image of a semiprime left Noetherian ring is proven to be a monomorphism, providing an affirmative answer to a question posed by Leroy and Matczuk.
