Sally Rooney is a contemporary Irish woman writer.Her novel Normal People shows the anxiety and struggle of Irish youth in the new era with her delicate and unique writing style.Centering on identity,this paper explor...Sally Rooney is a contemporary Irish woman writer.Her novel Normal People shows the anxiety and struggle of Irish youth in the new era with her delicate and unique writing style.Centering on identity,this paper explores the phenomenon of identity loss and the process of identity construction caused by the urban-rural and class differences of the characters in the book,and analyzes the new confusion and demands of Irish millennials in the context of globalization.展开更多
In a Cohen-Macaulay local ring(A,m),we study the Hilbert function of an integrally closed m-primary ideal I whose reduction number is three.,With a mild assump-tion we give an inequality ιA(A/I)≥e0(I)-e1(I)+(e2(I)+l...In a Cohen-Macaulay local ring(A,m),we study the Hilbert function of an integrally closed m-primary ideal I whose reduction number is three.,With a mild assump-tion we give an inequality ιA(A/I)≥e0(I)-e1(I)+(e2(I)+lA(I^(2)/QI)/2,where ei(I)denotes the ith Hilbert coeficient and Q denotes a minimal reduction of I.The inequality is located between inequalities of Itoh and Elias-Valla.Furthermore,this inequality be-comes an equality if and only if the depth of the associated graded ring of I is larger than or equal to dim A-1.We also study the Cohen-Macaulayness of the associated graded rings of determinantal rings.展开更多
文摘Sally Rooney is a contemporary Irish woman writer.Her novel Normal People shows the anxiety and struggle of Irish youth in the new era with her delicate and unique writing style.Centering on identity,this paper explores the phenomenon of identity loss and the process of identity construction caused by the urban-rural and class differences of the characters in the book,and analyzes the new confusion and demands of Irish millennials in the context of globalization.
基金Supported by JSPS KAKENHI Grant Number JP19J10579 and JP21K13766。
文摘In a Cohen-Macaulay local ring(A,m),we study the Hilbert function of an integrally closed m-primary ideal I whose reduction number is three.,With a mild assump-tion we give an inequality ιA(A/I)≥e0(I)-e1(I)+(e2(I)+lA(I^(2)/QI)/2,where ei(I)denotes the ith Hilbert coeficient and Q denotes a minimal reduction of I.The inequality is located between inequalities of Itoh and Elias-Valla.Furthermore,this inequality be-comes an equality if and only if the depth of the associated graded ring of I is larger than or equal to dim A-1.We also study the Cohen-Macaulayness of the associated graded rings of determinantal rings.
