If R is a 2-sided fir (free ideal ring) with no non-trivial right invariant elements, we shall find that the non-zero 2-sided ideals of R, under the usual multiplication of ideals, form a free semigroup with 1. In particular, this holds when R is a free associative algebra over a field. (We also consider the operations of multiplying right ideals by 2-sided ideals to get right ideals, 2-sided i...

in this paper rst we dene the notions of positive implicativehyper mv -ideals of types 1,2,3 and 4 in hyper mv -algebras and we investigatethe relationship between of them . then by some examples we show that thesenotions are not equivalent. finally we give some relations between these notionsand the notions of (weak) hyper mv -ideals and (weak) hyper mv -deductivesystems of hyper mv -algebras.

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

Introduction. There has arisen in recent years a substantial body of work on “multiplier ideals” in commutative rings (see [La]). Multiplier ideals are integrally closed ideals with properties that lend themselves to highly interesting applications. One is tempted then to ask just how special multiplier ideals are among integrally closed ideals in general. In this note we show that in a two-dim...

Abstract: In this paper we define the concept of (∈, ∈ ∨qk)-intuitionistic fuzzy h-ideals, (∈, ∈ ∨qk)-intuitionistic fuzzy h-bi-ideals, (∈, ∈ ∨qk) ∗-intuitionistic fuzzy h-quasi-ideals of hemiring. And also characterized h-hemiregular and h-intra-hemiregular hemiring by the properties of these (∈, ∈ ∨qk)-intuitionistic fuzzy h-ideals, (∈, ∈ ∨qk)-intuitionistic fuzzy h-bi-ideals, and (∈, ∈ ∨qk)i...

Professional skills are vital to preparing engineers for their careers, but how well do we teach and assess them in our professional programs? Many design faculty are unclear about the required skills, how to develop them, and how to assess them. In response to this need, the Integrated Design Engineering Assessment and Learning System (IDEALS) promotes professional skills in a semi-authentic c...

This is not the case in general. There are examples already with M = I such that reg(I) > 2 reg(I), see Sturmfels [15] and Terai [16]. On the other hand, Chandler [5] and Geramita, Gimigliano and Pitteloud [11] have shown that reg(I) ≤ k reg(I) holds for ideals with dimR/I ≤ 1. In general one has that reg(I) is asymptotically a linear function of k, see [14, 8]. If one takes I = m and M any gra...