semi-linear space; semiring; BL-algebra; MV-algebra; linear dependence

The notion of a linear space is generalized to the case where the underlying algebra is a commutative monoid and the set of scalars is a semiring reduct of a BL-algebra or an MV-algebra. The notions of linear dependence and independence are also introduced and necessary and sufficient conditions when vectors form a basis of a semi-linear space are given.

The notion of a linear space is generalized to the case where the underlying algebra is a commutative monoid and the set of scalars is a semiring reduct of a BL-algebra or an MV-algebra. The notions of linear dependence and independence are also introduced and necessary and sufficient conditions when vectors form a basis of a semi-linear space are given.