Related papers: Patterns of ideals of numerical semigroups
Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of…
In the first section of this paper, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Pr\"{u}fer semirings and characterize them in terms…
This book has seven chapters. In chapter one we give the basics needed to make this book a self contained one. Chapter two introduces the notion of interval semigroups and interval semifields and are algebraically analysed. Chapter three…
We introduce the concept of relational depth of a finite semigroup $S$ whose $J$-classes form a chain. It captures how far down in the ideal structure one is obliged to go in order to define the semigroup by generators and defining…
In this paper, we aim to introduce and study the notion of Endo-prime hyperideals.
We study the universal groups of inverse semigroups associated with point sets and with tilings. We focus our attention on two classes of examples. The first class consists of point sets which are obtained by a cut and projection scheme…
We provide a new and much simpler structure for quasi-ideal adequate transversals of abundant semigroups in terms of spined products, which is similar in nature to that given by Saito for weakly multiplicative inverse transversals of…
The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…
Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the…
In this paper we introduce the new concepts of supersymmetric and self-symmetric gaps of a numerical semigroup with two generators. Those concepts are based on certain symmetries of the gaps of the semigroup with respect to their Wilf…
We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the $r^{th}$ Feng-Rao number is obtained.
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…
This is a study of universal problems for semimodules, in particular coequalizers, coproducts, and tensor products. Furthermore the structure theory of semiideals of the semiring of natural numbers is extended.
The theory of ternary $\Gamma$-semirings extends classical ring and semiring frameworks by introducing a ternary product controlled by a parameter set $\Gamma$. Building on the foundational axioms recently established by Rao, Rani, and…
In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with finite Rees or Green index. Specific properties under…
We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional…
We give an explicit set of generators for the semigroup of the Gr\"obner degeneration of a toric ideal. This set of generators is used to study algebraic properties of the semigroup it generates: approximation of semigroups,…
We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future…
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…