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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of Tropical Biodiversity and Biotechnology REINWARDTIA BERITA BIOLOGI Biosaintifika: Journal of Biology & Biology Education Imajiner: Jurnal Matematika dan Pendidikan Matematika Journal Mathematics Education Sigma [JMES] Buitenzorg: Journal of Tropical Science
DIAN LATIFAH, DIAN
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Journal : CAUCHY: Jurnal Matematika Murni dan Aplikasi

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Order Ideals on Lexicographic Direct Sum of Three Totally Ordered Abelian Groups Latifah, Dian; Gozali, Sumanang Muhtar; Rosjanuardi, Rizky; Albania, Imam Nugraha
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i1.24116

Abstract

Order ideals play an important role in the study of abstract algebra, especially in the study of ordered groups. In this paper, we focus on the study of order ideals in lexicographic direct sums of totally ordered Abelian groups. We begin by examining the order ideals in the group of integers , and the group of real numbers  It is shown that there are no non-trivial order ideals in both groups. Next, we revisit the order ideals in the lexicographic direct sum of two totally ordered Abelian groups,  The only non-trivial order ideal of  is  Furthermore, our study extends to the lexicographic direct sum of three totally ordered Abelian groups:  and  We investigate the non-trivial order ideals in these structures. It is stated that the non-trivial order ideals of  are only  and  Furthermore, the non-trivial order ideals of  are only  and .Keywords: order ideal; lexicographic order; direct sum.
Co-Authors Albania, Imam Nugraha Budianti, Noviana Damayanti, Frisca Dian Rosleine, Dian Esti Munawaroh Fitri Kurniawati Hadiwiyono, Supandi Helmanto, Hendra Irsyam, Arifin Surya Dwipa JOSEPH A. HOLTUM, JOSEPH A. Muhammad Prayito Muhammad Rifqi Hariri Musyarofah Zuhri Noviady, Ikhsan Peniwidiyanti, Peniwidiyanti Purwantoro, RS Rahmaningtiyas, Lutfi Rasiman Rasiman Ria Windi Lestari Rizky Rosjanuardi ROBERT A. CONGDON, ROBERT A. Saripudin Saripudin Sri Hartini Sugiyono, Eko Suhaya, Yoyo Suhendri, Yudi Sulistyawati, Endah Sumanang Muhtar Gozali Wawangningrum, Hary Widjaya, Aulia Hasan Yudaputra, Angga Yuliyanto, Ponco Zulkarnaen, Rizmoon Nurul