报告人：Alberto Facchini 教授

工作单位：意大利帕多瓦大学

举办单位：数学学院

报告人简介：Alberto Facchini，意大利帕多瓦大学教授，1998年取得帕多瓦大学博士学位，研究领域包括环论、同调理论等，已经在代数类顶级期刊J. Algebra, J. Pure Appl. Algebra, Comm. Algebra, J. Algebra Appl.等期刊上发表80多篇论文，目前担任Comm. Algebra杂志的编委。

（1）

报告时间：2023年10月27日（星期五）17:00-18:00

报告地点：Zoom会议：973 8265 9639, PIN:888

报告简介：The aim of this paper is to investigate the behaviour of prime and semiprime subgroups of groups, and their relation with the existence of abelian normal subgroups. In particular, we study the set Spec(G) of all prime subgroups of a group G endowed with the Zariski topology and, among other examples, we construct an infinite group whose proper normal subgroups are prime and form a descending chain.

（2）

报告时间：2023年10月28日（星期六）17:30-18:30

报告地点：腾讯会议：686-584-706

报告简介：We describe the structure of projective covers of modules over a local ring, when such covers exist, and modules with minimal sets of generators. The case of modules over valuation rings is studied in more detail.

（3）

报告时间：2023年11月1日（星期三）17:30-18:30

报告地点：腾讯会议：368-722-267

报告简介：The main purpose of this paper is a wide generalization of one of the results abstract algebraic geometry begins with, namely of the fact that the prime spectrum Spec(R) of a unital commutative ringRis always a spectral topological space. In this generalization, which includes several other known ones. In fact when no further conditions on L are required, the resulting space can be and is only shown to be sober, and we discuss further conditions sufficient to make it spectral. This discussion involves establishing various comparison theorems on so-called prime, radical, solvable, and locally solvable elements of L; we also make short additional remarks on semiprime elements. We consider categorical and universal-algebraic applications involving general theory of commutators, and an application to ideals in what we call the commutative world. The cases of groups and of non-commutative rings are briefly considered separately.

（4）

报告时间：2023年11月3日（星期五）17:30-18:30

报告地点：腾讯会议：618-154-666

报告简介：We continue our study of the relation between existence of projective covers and existence of minimal sets of generators for right modules over an arbitrary ring.

（5）

报告时间：2023年11月6日（星期一）17:30-18:30

报告地点：腾讯会议：543-668-628

报告简介：We apply minimal weakly generating sets to study the existence of Add(U_R)-covers for a uniserial module. Moreover, we study endomorphism rings of artinian uniserial modules giving several examples.