In this paper, the explicit form of maximal elements, known as shorted operators, in a subring of a von Neumann regular ring has been obtained. As an application of the main theorem, the unique shorted operator (of electrical circuits) which was introduced by Anderson-Trapp has been derived.

Jacobson's generalization [5, Theorem 8] of Wedderburn's theorem [8] states that an algebraic division algebra over a finite field is commutative. These algebras have the property that some power2 of each element lies in the center. Kaplansky observed in [7] that any division ring, or, more generally, any semisimple ring, in which some power of each element lies in the center is commutative. Ka...

For each nontrivial semisimple Hopf algebra H of dimension sixteen over $\mathbb {C}$ , the smallest inner-faithful representation acting on a quadratic AS regular A 2 or 3, homogeneously and preserving grading, is determined. Each invariant subring AH When also regular, thus providing generalization Chevalley–Shephard–Todd Theorem, we say that reflection for A.

This paper focuses on the set-oriented operations and algebraic structures of soft sets. Relatedly, in this paper, firstly some essential properties $\alpha$-intersection set are investigated, where $\alpha$ is a non-empty subset universal set. Later, by using set, notion set-generated subring ring introduced. The generators intersections products subrings given. Some related about investigated...

This paper introduces the expanded real numbers as an ordered subring of hyperreal number field that does not contain any infinitesimals, and defines set all integrable functions from to numbers. allows identify Dirac delta with a special hyperreal-valued function variable: thus defined is general tool, applicable for mathematical modeling physical systems in which infinitely high densities occ...

Let $R$ and $S$ be commutative rings with unity, $f\colon R\rightarrow S$ a ring homomorphism $J$ an ideal of $S$. Then the subring $R\bowtie ^fJ:=\lbrace (a,f(a)+j)\mid a\in R$ $j\in J\rbrace $ $R\times is called amalgamation along respect to $f$. In this paper, we determine when ^fJ$ (generalized) filter ring.

Let R be an o-minimal expansion of a group in language which Th(R) eliminates quantifiers, and let C predicate for valuational cut R. We identify condition that implies quantifier elimination Th(R,C) the expanded by small number constants, which, turn, is implied having being universally axiomatizable. The applies example case when convex subring field its residue o-minimal.

In this paper, we prove that a linear action of a reductive group on a polynomial ring with good ltrations over a eld of characteristic p > 0 yields a strongly F-regular (in particular, Cohen-Macaulay) invariant subring. The strongly F-regular property of some known examples of invariant subrings, such as the coordinate rings of Schubert varieties in Grassmannians, are recovered. A similar resu...

Let R be an o-minimal field with a proper convex subring V . We axiomatize the class of all structures (R, V ) such that kind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in [8] it was shown that certain first order conditions on (R, V ) are sufficient for the o-minimality of kind. Here we prove that these conditions are also ...