The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...

In this paper, we extend the notion of tree language quotients to bottom-up quotients. Instead of computing the residual of a tree language from top to bottom and producing a list of tree languages, we show how to compute a set of k-ary trees, where k is an arbitrary integer. We define the quotient formula for different combinations of tree languages: union, symbol products, compositions, itera...

In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.

The functorial structure of type constructors is the foundation for many definition and proof principles in higher-order logic (HOL). For example, inductive coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class well-behaved constructors. Composition, fixpoints, and, under certain conditions, subtypes are known to preserve BNF structure. In this article, we t...

This paper examines the one-to-one-to-one correspondence between threshold graphs, Betti numbers of quotients polynomial rings by $2$-linear ideals, and anti-lecture hall compositions. In particular, we establish new explicit combinatorial mappings each these classes objects calculate expected values composition corresponding to a random graph.

We have determined composition series of a class induced representations appearing in Mœglin–Tadić classification discrete series. The result is further used to determine the certain from Langlands quotients. This should provide more information on decomposing standard as well Jacquet modules series, which has applications automorphic forms.

Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...

In this article, we define and study the class of simple transitive 2-representations of finitary 2-categories. We prove a weak version of the classical Jordan-Hölder Theorem where the weak composition subquotients are given by simple transitive 2-representations. For a large class of finitary 2-categories we prove that simple transitive 2-representations are exhausted by cell 2-representations...

Let Λ be a finite dimensional algebra over an algebraically closed field, and S a finite sequence of simple left Λ-modules. Quasiprojective subvarieties of Grassmannians, distinguished by accessible affine open covers, were introduced by the authors for use in classifying the uniserial representations of Λ having sequence S of consecutive composition factors. Our principal objectives here are t...