Related papers: Smarandache Near-rings
We introduce several commutative rings, the snake rings, that have strong connections to cluster algebras. The elements of these rings are residue classes of unions of certain labeled graphs that were used to construct canonical bases in…
We introduce a ring and a field, generated by a semigroup, and we investigate some of their properties.
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
The structural inversion asymmetry-induced spin-orbit interaction of conduction band electrons in zinc-blende and wurtzite semiconductor structures is analysed allowing for a three-dimensional (3D) character of the external electric field…
We propose new structures called almost o-minimal structures and $\mathfrak X$-structures. The former is a first-order expansion of a dense linear order without endpoints such that the intersection of a definable set with a bounded open…
We give an example of a non-noetherian quasi-analytic ring constructed using a quasi-analytic Denjoy-Carleman class. If we denote by $ \mathcal{D}_n$ the ring of those $ C^\infty$ quasianalytic function germs at $0\in \mathbb{R}^n$ which…
This work is a review of results about centrally essential rings and semirings. A ring (resp., semiring) is said to be centrally essential if it is either commutative or satisfy the property that for any non-central element $a$, there exist…
If two loops are isomorphic, then it is shown that their holomorphs are also isomorphic. Conversely, it is shown that if their holomorphs are isomorphic, then the loops are isotopic. It is shown that a loop is a Smarandache loop if and only…
Close binary stars are binary stars where the component stars are close enough such that they can exchange mass and/or energy. They are subdivided into semi-detached, overcontact or ellipsoidal binary stars. A challenging problem in the…
For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…
On the transversals of a subgroup of a group, using the binary operation of the group, structural mappings are defined. Based on these mappings, the notion of the hypergroup over the group is introduced, which generalizes the notion of the…
Recognizing when a ring is a complete matrix ring is of significant importance in algebra. It is well-known folklore that a ring $R$ is a complete $n\times n$ matrix ring, so $R\cong M_{n}(S)$ for some ring $S$, if and only if it contains a…
The majority of star formation results in binaries or higher multiple systems, and planets in such systems are constrained to a limited range of orbital parameters in order to remain stable against perturbations from stellar companions.…
A binary operation on any set induces a binary operation on its subsets. We explore families of subsets of a group that become a group under the induced operation and refer to such families as power groups of the given group. Our results…
A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces…
This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying…
This paper addresses the question: given a scalar group, can we determine all the additions that transform this scalar group into a (near-)field? A key approach to addressing this problem involves transporting (near-)field structures via…
The aim of this text is to provide a clear description of the theory of Infra-nilmanifolds and their fundamental groups, the almost-Bieberbach groups. For most of the proofs of the results, we refer to the literature. Nevertheless, at…
This note is a continuation of the paper [2] (see references). We describe some natural pseudogroup structures on almost complex manifolds of type $m$. A kind of coherency is discussed for the sheaf of almost holomorphic functions.