... 1. Introduction. The nearrings considered here are **right** nearrings. For in- formation about abstract nearrings, one may consult [1, 4, 5]. An n-dimensional Euclidean nearring is any topological nearring whose ...

... i = 1 which are also **right** ideals of the nearring satisfying several additional properties. Speciﬁcally, for each w ∈ ᏺ n , we require that there exist w i ∈ J i , 1 ≤ i ≤ n, such that w = w 1 + w 2 + ··· + w n ...

... interior **ideal** of T, f ( xaxyz ) ∨ λ ≥ f ( x ) ∧ ...-fuzzy **right** **ideal** of ...left **ideal** of T and f is a ( λ, µ ) -fuzzy lateral **ideal** of ...-fuzzy **ideal** of ...

... The aim of this paper is to introduce and study the notions of M-fuzzy quantic nuclei and conuclei on quantales. Firstly, the concept of an M-fuzzy quantic nuclei is introduced and some of its properties are discussed. ...

... left **ideal** of R we have eΓL ⊆ L and eΓL ⊆ eΓR implies eΓL ⊆ L ∩ ...left **ideal** and x ∈ ...left **ideal** and eΓR is a **right** **ideal** of R, we get L ∩ (eΓR) is a quasi-**ideal** of R by ...

... Proof First of all, since A is a **right** **ideal** and B is a left **ideal** of S, the intersection A ∩ B is nonempty. Indeed: Take an element a ∈ A and an element b ∈ B (A, B 6= ∅); then a ◦ b ⊆ A ∗ B ⊆ A ∗ S ...

... fuzzy **ideal** of a ring. The notions of fuzzy sub near-ring, fuzzy **ideal** and fuzzy N- subgroup of a near-ring were introduced by Salah Abou-Zaid [11] and it has been studied by several ...bi- **ideal** of ...

... (resp. **right**) duo if and only if it is fuzzy left (resp. fuzzy **right**) ...a **right** (resp. left) **ideal** if and only if every fuzzy bi-**ideal** is a fuzzy **right** ...left) **ideal**. In ...

... (i) **right** **ideal** implies left **ideal** and vice versa, (ii) for two ideals M and N of S, (a) M N is an **ideal** and (b) M N and N M are connected ...every **ideal** of S is prime and the set of ...

... every **right** (left) annihilator **ideal** is generated by an ...the **right** annihilator of every **right** **ideal** is generated (as a **right** **ideal**) by an ...principal **right** ...

... (resp. **right**) **ideal** of R if a + b ∈ I, ra ∈ I ...and **right** **ideal** of R, then I is called an **ideal** of ...an **ideal** I of R is said to be ∗-**ideal** if I ∗ ⊆ ...sided **ideal** ...

... Proof. Let R be a **right** **ideal**, M be a lateral **ideal**, and L be a left **ideal** of S such that Q = R ∩ M ∩ L. Then, by Lemmas 3.3 and 3.7, we find that Q is a quasi-**ideal** of S. The converse ...

... (**right**) **ideal** of an ordered Γ−semiring M if A is closed under addition, M ΓA ⊆ A (AΓM ⊆ A) and if for any a ∈ M, b ∈ A, a ≤ b ⇒ a ∈ ...an **ideal** of M if it is both a left **ideal** and a ...

... this trivial case, every maximal **right** **ideal** and maximal left **ideal** of S is two-sided. Rings in which all maximal **right** ideals and maximal left ideals are two-sided are called quasi- duo. ...

... others. Due to these possibilities of applications, semigroups and related structures are presently extensively investigated in fuzzy settings (see e.g., monograph [18]). In particular (fuzzy) regular ordered semigroups, ...

... a **right** **ideal** in a fusion system F on a ﬁnite p-group P denote by S < (C) the full subcategory of all σ : [m] → C in S(C) such that for 0 ≤ i < j ≤ m ...

... Proof. Let G be a **right** R-group. Suppose that G is monogenic. Let g be a generator of G. Define h : R → G by h(r) = gr, for all r ∈ R. h is an R-homomorphism of R onto G. Let K be the kernel of h. K = { r ∈ R | ...

... a **right** Kasch ring if any simple **right** R-module is isomorphic to a minimal **right** **ideal** of ...is **right** Kasch if and only if every maximal **right** **ideal** of R is a **right** ...

... This note is motived by the previous cited results. Our main theorem gives a general- ization of Lanski’s result to the case when (dδ) is a Lie derivation of the subset [I,I ] into R, where I is a nonzero **right** ...

... Proof: If R is a primitive weakly standard ring, then it contains regular maximal right ideal E which contains no two- sided ideal of R other than zero ideal.. If A=0 then R is associat[r] ...