Characterization of obstinate HvMV-ideals.

One motivation to study obstinate ideals in any algebra of logic is that the induced quotient algebra by these ideals is the two-element Boolean algebra. In this paper, we introduce two types of obstinate ideals in HvMV-algebras; obstinate HvMV-ideals and obstinate weak HvMV-ideals. Giving several theorems and examples we characterize these HvMV-ideals. For example, we prove that an HvMV-ideal (if exists) must be maximal, and any HvMV-algebra with odd number of elements does not contatin an obstinate HvMV-ideal. Also, we characterize these HvMV-ideals in finite HvMV-algebras with at most six elements; we investigate that which subsets can be an obstinate (weak) HvMV-ideal. In the sequel, we investigate the relationships between obstinate (weak) HvMV-ideals, and Boolean and prime HvMV-ideals. Finally, we prove that in a commutative HvMV-algebra, the quotient HvMV-algebra induced by an obstinate weak HvMV-ideal must be a two-elements Boolean algebra. [ABSTRACT FROM AUTHOR]