Transpose of a Module Relative to its Nonzero Submodule
Yudi Mahatma (a*), Ibnu Hadi (a), Sudarwanto (a)

a) Program Studi Matematika, FMIPA, Universitas Negeri Jakarta
Jalan Rawamangun Muka Raya RT 11/RW 14, Pulo Gadung, Jakarta Timur 13220, Indonesia
*yudi_mahatma[at]unj.ac.id

Abstract

Let K be algebraically closed field and A be finite dimensional K-algebra. It has been shown that any right A-module M admits projective cover and thus admits a minimal projective presentation that induces the transpose of M. In 2017, Mahatma and Muchtadi-Alamsyah introduced the notion of the U-projective resolution which is the generalization of the concept of projective resolution. Let M be right A-module and U be nonzero submodule of M. Using the idea of U-projective resolution, we define the minimal U-projective presentation of M that induces the transpose of M relative to U. We investigate some properties of the modified transpose.

Keywords: algebraically closed field- algebra- minimal projective presentation- transpose

Topic: Mathematics