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Homomorphisms of Modules over Two Skew Generalized Power Series Rings Ahmad Faisol; Fitriani Fitriani; Muslim Ansori; Budi Surodjo
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1921

Abstract

Let R and R' be rings with identity and let S be a strictly ordered monoid equipped with twisting homomorphisms into the endomorphism rings of R and R'. Using these data, we consider two skew generalized power series rings associated with R and R'. Starting from an (R,R')-module M, we construct an induced module consisting of generalized power series with coefficients in M and show that it naturally becomes a module over the two skew generalized power series rings through a suitable trilinear action. We then study homomorphisms in this framework. In particular, we prove that every (R,R')-module homomorphism between two modules induces a corresponding homomorphism between their associated generalized power series modules. Furthermore, we provide sufficient conditions describing when a generalized power series belongs to the kernel of the induced homomorphism in terms of the coefficientwise behavior of the original map. These results extend the theory of skew generalized power series modules from the classical single-ring setting to a two-ring context and provide a foundation for further developments, including generalized isomorphism results and related algebraic applications.
Co-Authors . Wamiliana Aang Nuryaman Adelia, Lisa Ahmad Faisol Ahmad Rizki Wiranto Akmal Junaidi Ambarwati, Yuli Ananto Adi Nugraha Andriani, Jessica Attiya Yuliana Azis, Dorrah Budi Surodjo Dania Azzahra David Aji Saputra Desiana Putri Dian Kurniasari Dian Kurniasari Dorrah Azis Dwiyanti, Gusti Ayu Fitri Ayuni Hafifullah, Desfan Indah Emilia Wijayanti Jessica Andriani Larasati Larasati Larasati Larasati Listiana Listiana Lucia Ratnasari M.G. Arma Yoga Pratama Mohamad Ibnu Hambali, Mohamad Ibnu Muammar, Muhammad Fikri Muslim Ansori Muslim Ansori Muslim Ansori Mustofa Usman Nevi Setyaningsih Nikken Prima Puspita Notiragayu Notiragayu Notiragayu Notiragayu, Notiragayu Nurlela Nurlela Pardede, Wesly Agustinus Purba, Tresya Carmela Rahma, Aira Rahmah Mutiara Ayu Ningtiyas Rahmawati, Rara Gusti Rinanda, Selvi Diana Dwi Rudi Ruswandi Rudi Ruswandi Sandi Saputra Setyaningsih, Nevi SHAKIR ALI Siti Khabibah Siti Laelatul Chasanah Siti Laelatul Chasanah Siti Laelatul Chasanah, Siti Laelatul Sitompul, Desi Elena Tresya Carmela Purba Trisnawati, Evi Utami, Bernadhita Herindri Samodera Waluyo, Ridho Wamiliana ., Wamiliana Wamiliana Wamiliana Wesly Agustinus Pardede Widiarti Widiarti Yesi Santika Yudi Antoni Yunita Septriana Anwar