Open AccessIdeals in bounded equality algebras
Author(s) -
Akbar Paad
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1907113p
Subject(s) - mathematics , stone's representation theorem for boolean algebras , ideal (ethics) , free boolean algebra , bounded function , complete boolean algebra , isomorphism (crystallography) , congruence (geometry) , boolean algebras canonically defined , prime (order theory) , pure mathematics , prime ideal , algebra over a field , boolean algebra , boolean prime ideal theorem , two element boolean algebra , discrete mathematics , algebra representation , combinatorics , mathematical analysis , philosophy , crystal structure , chemistry , geometry , epistemology , crystallography
In this paper, the concept of ideal in bounded equality algebras is introduced. With respect to this concepts, some related results are given. In particular, we prove that there is an one-to-one corresponding between congruence relation on an involutive equality algebra and the set of ideals on it. Also, we prove the first isomorphism theorem on equality algebras. Moreover, the notions of prime and Boolean ideals in equality algebras are introduced. Finally, we prove that ideal I of involutive prelinear equality algebra E is a Boolean ideal if and only if E/I is a Boolean algebra.