1.1. Strictly Cyclic Modules and Modular Right Ideals. For a ring A with identity, cyclic modules are precisely those of the form a\A where a is a right ideal. What might be a useful analogous statement for a ring without identity? This question motivates what follows in this subsection. A module M is strictly cyclic if there exists m in M such that mA = M (such an m is called a generator); a r...

In the theory of modules over commutative rings there are several possibilities of defining associated prime ideals. The usual definition of an associated prime ideal p for a module M is that p is the annihilator of an element of M . In [2] §1 exercise 17 a generalization of this notion is given. p is called weakly associated (faiblement associé) to M if p is minimal in the set of the prime ide...

A calyx (multiplicative lattice) is a complete lattice endowed with the structure of a monoid such that multiplication by an element is a left adjoint functor of complete lattices (equivalently, a left adjoint functor which preserves colimits). Calyxes are a generalization of the set of ideals of a ring, which form a complete lattice under intersection and summation; in conjunction with the nat...

Let 9t and © be commutative rings such that © contains, and has the same identity element as, 9Î. If p and $ are prime ideals in SK and © respectively such that ^P\9t = p then we shall say that $ lies over, or contracts to, p. If over every prime ideal in dt there lies a prime ideal in ©, we shall say that the "lying-over" theorem holds for the pair of rings 9Î and ©. Suppose now that q and p a...

Peroxisome proliferator-activated receptor-α (PPARα), a nuclear receptor, plays an important role in the transcription of genes involved in fatty acid metabolism through heterodimerization with the retinoid x receptor (RXR). The consensus sequence of the PPAR response element (PPRE) is composed of two AGGTCA-like sequences directionally aligned with a single nucleotide spacer. PPARα and RXR bin...

In this paper a simple algebraic formula is obtained for the correspondence between finite right nilpotent Fp-braces and pre-Lie algebras. This agrees with using Lazard's algebras proposed by Wolfgang Rump in 2014. As an application example, classification of all generated one element cardinality p4 obtained. It also shown that sum number left ideals brace ideal, therefore every contains larges...

in this work, an inverse finite element formulation was modified for considering material anisotropy in obtaining blank shape and forming severity of deep drawn orthotropic parts. in this procedure, geometry of final part and thickness of initial blank sheet were known. after applying ideal forming formulations between material points of initial blank and final shape, an equation system was obt...

the design of packaging is an important factor in selling any products, which should be done based on the customers taste, in a way that influence the costumers in a few seconds and persuades them to buy an special product. in this article, first the integrity of bordio’s theory in iranian community is tested and after proving the correctionand utility of this theory, we attempts to extract the...

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...