Let P be a polynomial over the ring of mod m integers. P weakly Abstract-1 represents Boolean function f : {0, 1}n → {0, 1} if there is a subset S ⊆ {0, 1, . . . , m − 1} such that f(x) = 0 if and only if P (x) ∈ S. The smallest degree of polynomials P weakly representing f is called the weak mod m degree of f . We give here an Ω(logn) lower bound for the weak degree of the generalized inner pr...

In a ternary semihyperring, addition is a hyperoperation and multiplicationis a ternary operation. Indeed, the notion of ternary semihyperringsis a generalization of semirings. Our main purpose of this paper is to introducethe notions of fuzzy hyperideal and fuzzy bi-hyperideal in ternary semihyperrings.We give some characterizations of fuzzy hyperideals and investigateseveral kinds of them.

Abstract We are interested in properties, especially injectivity (in the sense of category theory), ternary rings operators generated by certain subsets an inverse semigroup via regular representation. determine all extended bicyclic which closed under triple product $$xy^*z$$ x y <...

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.

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...