Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

The concept of the Jacobson radical of a ring is generalized to semirings. A semiring is a system consisting of a set S together with two binary operations, called addition and multiplication, which forms a semigroup relative to addition, a semigroup relative to multiplication, and the right and left distributive laws hold. The additive semigroup of S is assumed to be commutative. The right ide...

A right ternary N -group (RTNG) over a right ternary near-ring N is a generalization of its binary counterpart and fuzzy soft sets are generalization of soft sets which are parameterized family of subsets of a universal set. In this paper fuzzy soft N -subgroups and N -ideals over right ternary N -groups are defined and their basic algebraic properties are studied. Fuzzy soft N -subgroups and N...

We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible decomposition of monomial ideals. The gap can be computed in polynomial time when the dimension is fixed.

Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or empty, then so does the graph product. Our second main result gives a presentation for the inverse hull of such a graph product. We then specialise to the ca...