Journal of Algebraic Structures and Their Applications
Volume:3 Issue: 2, Summer - Autumn 2016

The notion of f-derivations of UP-algebras is introduced, some useful examples are discussed, and related properties are investigated. Moreover, we show that the fixed set and the kernel of f-derivations are UP-subalgebras of UP-algebras,and also give examples to show that the two sets are not UP-ideals of UP-algebras in general.

Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

In this paper, we introduce the notions of expansion of ideals in MV-algebras, (τ,σ)−primary, (τ,σ)-obstinate and (τ,σ)-Boolean in MV−algebras. We investigate the relations of them. For example, we show that every (τ,σ)-obstinate ideal of an MV− algebra is (τ,σ)-primary and (τ,σ)-Boolean. In particular, we define an expansion σy of ideals in an MV−algebra. A characterization of expansion ideal with respect to σy is given. Finally, we show that the class C(σy) of all constant ideals relative to σy is a Heyting algebra.

By considering the notion of MV-algebras, we recall some results on enumeration of MV-algebras and we carry out a study on characterization of MV-algebras of orders 2, 3, 4, 5, 6 and 7. We obtain that there is one non-isomorphic MV-algebra of orders 2, 3, 5 and 7 and two non-isomorphic MV-algebras of orders 4 and 6.

Recently, a new parameter of a code, referred to as the remoteness, has been introduced.
This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group U6n as a subgroup of S2n and obtain its remoteness. We show that the remoteness of the permutation code U6n is 2n. Moreover, it is proved that the covering radius of U6n is also 2n.