On subalgebras of MS-algebras

Abstract In this paper, we introduce the concepts of subalgebras, principal subalgebras and $$d_{L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> -subalgebras of a principal MS -algebra and describe the lattices of such subalgebras. Also, we describe a subalgebra [ S ] that generated by a subset S of an MS -algebra (principal MS -algebra) L and study related properties. Finally, we determine and characterize the principal subalgebras of a principal MS -algebra via admissible pairs.