Lattice of full soft Lie algebra
Author(s):
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
In this paper, we study the relation between the soft sets and soft Lie algebras with the lattice theory. We introduce the concepts of the lattice of soft sets, full soft sets and soft Lie algebras and next, we verify some properties of them. We prove that the lattice of the soft sets on a fixed parameter set is isomorphic to the power set of a set with respect to set inclusion. In particular, we characterize the atoms in the lattice of the soft sets and the lattice of full soft Lie algebras. After that, we introduce the compact elements in the full soft Lie algebras and we present the necessary and sufficient conditions for the compactness and atomicness of the lattice of full soft Lie algebras. We show that if a full soft Lie algebra is a compact element of the lattice of full soft Lie algebra then the parameter set is finite and the Lie algebra is finitely generated. In the sequel, we study the relationship between prime and maximal ideals in Lie algebras and the prime and maximal elements in the lattice of soft Lie algebras.
Keywords:
Language:
Persian
Published:
New research in Mathematics, Volume:4 Issue: 15, 2018
Pages:
93 to 104
magiran.com/p1916894
دانلود و مطالعه متن این مقاله با یکی از روشهای زیر امکان پذیر است:
اشتراک شخصی
با عضویت و پرداخت آنلاین حق اشتراک یکساله به مبلغ 1,390,000ريال میتوانید 70 عنوان مطلب دانلود کنید!
اشتراک سازمانی
به کتابخانه دانشگاه یا محل کار خود پیشنهاد کنید تا اشتراک سازمانی این پایگاه را برای دسترسی نامحدود همه کاربران به متن مطالب تهیه نمایند!
توجه!
- حق عضویت دریافتی صرف حمایت از نشریات عضو و نگهداری، تکمیل و توسعه مگیران میشود.
- پرداخت حق اشتراک و دانلود مقالات اجازه بازنشر آن در سایر رسانههای چاپی و دیجیتال را به کاربر نمیدهد.
In order to view content subscription is required
Personal subscription
Subscribe magiran.com for 70 € euros via PayPal and download 70 articles during a year.
Organization subscription
Please contact us to subscribe your university or library for unlimited access!