in recent years cryptography has played a big role especially in computer science for information security block cipher and public

   In this paper ,we introduce a concept of Max– module as follows: M is called a Max- module if ann N R is a maximal ideal of R, for each non– zero submodule N of M;       In other words, M is a Max– module iff (0) is a *- submodule, where  a proper submodule N of M is called a *- submodule if [ ] : N K R is a maximal ideal of R, for each submodule K contains N properly.       In this paper, some properties and characterizations of max– modules and  *- submodules are given. Also, various basic results a bout Max– modules are considered. Moreover, some relations between max- modules and other types of modules are considered.

Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called Z-regular if every cyclic submodule (equivalently every finitely generated) is projective and direct summand. And a module M is F-regular if every submodule of M is pure. In this paper we study a class of modules lies between Z-regular and F-regular module, we call these modules regular modules.

Inˑthis work, we introduce the algebraic structure of semigroup with KU-algebra is called KU-semigroup and then we investigate some basic properties of this structure. We define the KU-semigroup and several examples are presented. Also,we study some types of ideals in this concept such as S-ideal,k- ideal and P-ideal.The relations between these types of ideals are discussed and few results for product S-ideals of product KU-semigroups are given. Furthermore, few results of some ideals in KU-semigroup under homomorphism are discussed.

      Let  be a right module over a ring  with identity. The semisecond submodules are studied in this paper. A nonzero submodule  of   is called semisecond if    for each . More information and characterizations about this concept is provided in our work.

The current study aimed to identify the difficulties faced by the student in mathematics and possible proposals to address these difficulties. The study used a descriptive method also used the questionnaire to collect data and information were applied to a sample of (163) male and female teachers. The results of the study found that the degree of difficulties in learning mathematics for the fifth and sixth grades is high for some paragraphs and intermediate for other paragraphs, included the student's field. The results also revealed that there were no statistically significant differences at the level of significance (α = 0.05) between the responses of the members of the study sample from male and female teachers to the degree of diffi

Foreign body embolization is a rare but serious iatrogenic complication that might necessitate transcatheter or even surgical retrieval. A broken double-lumen catheter was snared using a goose neck snare kit. The procedure was successful, and the patient experienced no further complications.

In this study new derivatives of Schiff bases 5-8, 1, 3-oxazepine 9-16 and tetrazoles 17-19 have been synthesized from the new starting material 1 which has synthesized the reaction of one mole of dichloro acetic acid and two moles of thiophenol, the esters 2-3 were synthesized from the reaction of compound 1 with methanol or ethanol respectively in the presence of H2SO4 as catalyst then 2, 2-dithiophenylaceto Hydrazide 4 were synthesized from the reaction of 2 or 3 with hydrazine hydrate 80%, Schiff bases 5-8 were synthesized from the reaction of 4 with appropriate aldehyde or ketone. Treatment of Schiff bases with maleic and phathalic anhydride in dry benzene to give 1, 3-oxazepen derivatives 9-16 and with sodium azide in tetrahydrofuran

The present investigation aims to determine the effects of aflatoxin B1 (AFB1) on biotransformation and antioxidant genes and the protective effects of curcumin, present in turmeric (Curcuma longa) powder (TMP). Specifically, the study included four groups of albino mice were fed for 30 days on diet Group I: Control, Group II: animals fed on the conventional basal diet supplemented with 0.5% food grade TMP that supplied 74 mg/kg total curcuminoids. Group III contained animals reared on conventional basal diet supplemented with 1.0 ppm AFB1 supplied by ground aflatoxin culture material (760 ppm AFB1). Finally, Group IV comprised of albino mice fed with basal diet supplemented with 1.0 ppm AFB1 and 0.5% TMP that supplied 74 mg/kg of the