The logic of bunched implications (BI), introduced by O’Hearn and Pym, is a substructural logic which freely combines additive and multiplicative implications. Boolean BI (BBI) denotes BI with classical interpretation of additives and its model is the commutative monoid. We show that when the monoid is finitely generated and propositions are recursively defined, or the monoid is infinitely gene...

A generalized arithemtic numerical monoid is of the form S = 〈a, ah+d, ah+2d, . . . , ah+ xd〉 where the gcd(a, d) = 1 and a > x. Much is known for the arithmetic numerical monoid, when h = 1, due to known information for that specific monoid’s length set. Therefore, this paper will explore various invariants of the generalized arithmetic numerical monoid.

We present an algebra for data-intensive scalable computing based on monoid homomorphisms that consists of a small set of operations that capture most features supported by current domain-specific languages for data-centric distributed computing. This algebra is being used as the formal basis of MRQL, which is a query processing and optimization system for large-scale distributed data analysis....

By a generalized Tannaka-Krein reconstruction we associate to the admissible representions of the category O of a Kac-Moody algebra, and its category of admissible duals a monoid with a coordinate ring. The Kac-Moody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the Kac-Moody group is the algebra of strongly regular functions introduced by ...

A subresiduated lattice ordered commutative monoid (or srl-monoid for short) is a with particular subalgebra which contains residuated implication. The srl-monoids can be regarded as algebras that generalize lattices and respectively. In this paper we prove the class of forms variety. We show congruences any isomorphic to its strongly convex subalgebras also give description generated by subset...

A Puiseux monoid is an additive submonoid of the nonnegative rational numbers. If M a monoid, then question whether each nonunit element can be written as sum irreducible elements (that is, atomic) surprisingly difficult. For instance, although various techniques have been developed over past few years to identify subclasses monoids that are atomic, no general characterization such known. Here ...

This paper considers the word problem for free inverse monoids of finite rank from a language theory perspective. It is shown that no free inverse monoid has context-free word problem; that the word problem of the free inverse monoid of rank 1 is both 2-context-free (an intersection of two context-free languages) and ET0L; that the co-word problem of the free inverse monoid of rank 1 is context...

We describe the local structure of an irreducible algebraic monoid M at an idempotent element e. When e is minimal, we show that M is an induced variety over the kernel MeM (a homogeneous space) with fibre the two-sided stabilizer Me (a connected affine monoid having a zero element and a dense unit group). This yields the irreducibility of stabilizers and centralizers of idempotents when M is n...

We show that if (M,⊗, I) is a monoidal model category then REnd M (I) is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2-monoid.

We state a simple condition on a rational subset X of a free monoid B for the existence of a sequential function that is a one-to-one mapping of some free monoid A onto X. As a by-product we obtain new sequential bijections of a free monoid onto another.