Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly a unital module over noncommutative ring with nonzero identity. This is new class between (weakly submodules) 2-absorbing submodules). Let R be identity $$1\ne 0$$ 1 ≠ 0 </mml:m...

Abstract The purposes of this paper are to introduce generalizations quasi-prime ideals the context $$\phi $$ ? -quasi-prime ideals. Let : {\mathcal {I}}(S) \rightarrow \cup \left\{ \emptyset \right\} : I ( S ) </m...

Abstract A Grigorchuk–Gupta–Sidki (GGS)-group is a subgroup of the automorphism group p -regular rooted tree for an odd prime , generated by one and directed automorphism. Pervova proved that all torsion GGS-groups do not have maximal subgroups infinite index. Here, we extend result to nontorsion GGS-groups, which include weakly regular branch, but GGS-group.

For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called “proper”. It is known that the Boolean semiring, the semiring of natural numbers, the ring of integers, all finite commutative positively ordered semirings and all fields are proper. The semiring S is Noetherian...

We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule Sn over a semiring S is rational if it has a generating family that is a rational subset of Sn, Sn being thought of as a monoid under the entrywise prod...

Spaces of orderings were introduced by the second author in a series of papers 15]{{19] and various structure results were obtained generalizing results proved earlier for formally real elds by various people: In 6] and 26] (also see 20] and 23] 25]) Craven and Tschimmel prove that formally real skew elds give rise to spaces of orderings. In 8] (also see 9]) Kalhoo extends this to ternary elds ...

We have recently shown that insulin-like growth factor (IGF)-binding protein 5 forms ternary complexes with IGF-I or IGF-II and the acid-labile subunit (ALS) (Twigg, S. M., and Baxter, R. C. (1998) J. Biol. Chem. 273, 6074-6079). Because IGF-binding protein 3 (IGFBP-3) binds to ALS through its basic carboxyl-terminal domain, we tested whether a homologous region present in IGFBP-5 is involved i...

We study the algebraic and arithmetic structure of monoids invertible ideals (more precisely, $r$-invertible $r$-ideals for certain ideal systems $r$) Krull weakly Mori domains. also investigate all nonzero polynomial rings with at least two indeterminates over noetherian Among others, we show that they are not transfer but share several arithmetical phenomena having infinite class group prime ...

Let [Formula: see text] text], be fixed. also text]. We prove on assumption of the Generalized Riemann Hypothesis that each sufficiently large odd integer can represented in form where are for and decimal expansion does not contain digit The proof merges methods Maynard from his paper infinitude primes with restricted digits, results Balog Friedlander Piatetski-Shapiro Hardy–Littlewood circle m...