Yudi Mahatma, Ibnu Hadi, Sudarwanto
Suppose that K is an algebraically closed field and A is a finite-dimensional K-algebra. It has been shown that any finitely generated 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 concept of the U-projective resolution as a generalization of the concept of projective resolution. Let M be a right A-module, and U be a 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. In the classic version, it is known that the transpose of a module M is zero if and only if M is projective. In this paper, we give the analogous result for the modified transpose. © 2024 American Institute of Physics Inc.. All rights reserved.
Program Studi Matematika, FMIPA, Universitas Negeri Jakarta, Jalan Rawamangun Muka Raya RT 11/RW 14, Pulo Gadung, Jakarta Timur, 13220, Indonesia
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