Let D be a 1-dimensional Prüfer domain with exactly two maximal ideals. We completely determine the star operations and the semistar operations on D. Let G be a torsion-free abelian additive group. If G is not discrete, G is called indiscrete. If every non-empty subset S of G which is bounded below has its infimum inf(S) in G, then G is called complete. If G is not complete, G is called incompl...

Let us assume we are given an almost left-null line ΣA,d. It was Darboux who first asked whether manifolds can be described. We show that every canonically d-smooth manifold is uncountable and conditionally reversible. U. De Moivre’s derivation of sub-totally null, essentially sub-reversible ideals was a milestone in non-standard number theory. Therefore recently, there has been much interest i...

Abstract Human endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms engineering, arts, sciences, medical social economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world involve many uncertainties making them difficult to by means. researchers world over have established new mathematical ...

Hermite normal form and Smith normal form are canonic forms of integral matrices with respect to congruence produced by multiplication with right unimodular matrix resp. by multiplication with left and right unimodular matrix simultaneously. This lower-diagonal resp. diagonal form has many applications in various elds. Unfortunately, the computation of them is extremely resource consuming. The ...

Let K be a field and X an m×n matrix of indeterminates over K. Let K[X] denote the polynomial ring generated by all the indeterminates Xij . For a given positive integer r ≤ min{m, n}, we consider the determinantal ideal Ir+1 = Ir+1(X) generated by all r + 1 minors of X if r < min{m, n} and Ir+1 = (0) otherwise. Let Rr+1 = Rr+1(X) be the determinantal ring K[X]/Ir+1. Determinantal ideals and ri...

Case Description- An eleven-year-old Golden retriever male dog (dog I) and a four-year-old neutered Toy Terrier (dog II) were referred to Small Animal Clinic. Dog I was suffered from   partial loss of vision and engorgement of episcleral vessels of his right eye and dog II was blind. Intraocular pressure (IOP) of right eye was 37.8 mmHg in dog  I  and 34.5 and 31.6 mmHg in the right and left...

The aim of this manuscript is to introduce the \((\alpha,\beta)\)-hesitant fuzzy set and apply it semigroups. In paper, as a generalization concept hesitant sets semigroup theory, subsemigroups semigroups introduced, related properties are discussed. Furthermore, we define study ideals on particular, investigate structure ideal generated by in semigroup. addition, also concepts semiprime semigr...

It is well-known that for the integral group ring of a polycyclic group several decision problems are decidable, in particular the ideal membership problem. In this paper we define an effective reduction relation for group rings over polycyclic groups. This reduction is based on left multiplication and hence corresponds to left ideals. Using this reduction we present a generalization of Buchber...

We study in detail the algebra Sn in the title which is an algebra obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. The algebra Sn is non-commutative and neither left nor right Noetherian but the set of its ideals satisfies the a.c.c., and the ideals commute. It is proved that the classical Krull dimen...

The main result of this paper gives a presentation for an arbitrary subgroup of a monoid defined by a presentation. It is a modification of the well known Reidemeister–Schreier theorem for groups. Some consequences of this result are explored. It is proved that a regular monoid with finitely many left and right ideals is finitely presented if and only if all its maximal subgroups are finitely p...