الغرض من هذا العمل هو دراسة الفضاء الإسقاطي ثلاثي الأبعاد PG (3، P) حيث p = 4 باستخدام المعادلات الجبرية وجدنا النقاط والخطوط والمستويات وفي هذا الفضاء نبني (k، ℓ) -span وهي مجموعة من خطوط k لا يتقاطع اثنان منها. نثبت أن الحد الأقصى للكمال (k، ℓ) -span في PG (3،4) هو (17، ℓ) -span ، وهو ما يساوي جميع نقاط المساحة التي تسمى السبريد.

In this paper, we define a cubic positive implicative-ideal, a cubic implicative-ideal and a cubic commutative-ideal of a semigroup in KU-algebra as a generalization of a fuzzy (positive implicative-ideal, an implicative-ideal and a commutative-ideal) of a semigroup in KU-algebra. Some relations between these types of cubic ideals are discussed. Also, some important properties of these ideals are studied. Finally, some important theories are discussed. It is proved that every cubic commutative-ideal, cubic positive implicative-ideal, and cubic implicative-ideal are a cubic ideal, but not conversely. Also, we show that if Θ is a cubic positive implicative-ideal and a cubic commutative-ideal then Θ is a cubic implicative-ideal. Some example

The aim of t his p aper is t o const ruct t he (k,r)-caps in t he p rojective 3-sp ace PG(3,p ) over Galois field GF(4). We found t hat t he maximum comp let e (k,2)-cap which is called an ovaloid, exist s in PG(3,4) when k = 13. Moreover t he maximum (k,3)-cap s, (k,4)-cap s and (k,5)-caps.

The purpose of this work is to study the classification and construction of (k,3)-arcs in the projective plane PG(2,7). We found that there are two (5,3)-arcs, four (6,3)-arcs, six (7,3)arcs, six (8,3)-arcs, seven (9,3)-arcs, six (10,3)-arcs and six (11,3)-arcs. All of these arcs are incomplete. The number of distinct (12,3)-arcs are six, two of them are complete. There are four distinct (13,3)-arcs, two of them are complete and one (14,3)-arc which is incomplete. There exists one complete (15,3)-arc.

In this work, we construct projectively distinct (k,3)-arcs in the projective plane PG(2,9) by applying a geometrical method. The cubic curves have been been constructed by using the general equation of the cubic. We found that there are complete (13,3)-arcs, complete (15,3)-arcs and we found that the only (16,3)-arcs lead to maximum completeness

In this paper, we introduce the concepts of positive implicative [resp. implicative and commutative] Γ-KU-algebras, and obtain their some properties (including characterizations) respectively and some relationships among them. Next, we propose the notions of positive implicative [resp. implicative and commutative] Γ-ideals of a Γ-KU-algebra, and deal with their some properties (including characterizations) respectively and some relationships among them. Finally, we define a topological Γ-KU-algebra and discuss its various topological structures.

In this work, we construct the projectively distinct (k, n)-arcs in PG (3, 4) over Galois field GF (4), where k 5, and we found that the complete (k, n)-arcs, where 3 n 21, moreover we prove geometrically that the maximum complete (k, n)-arc in PG (3, 4) is (85, 21)-arc. A (k, n)-arcs is a set of k points no n+ 1 of which are collinear. A (k, n)-arcs is complete if it is not contained in a (k+ 1, n)-arcs

In this paper we introduce the basic of definitions of groups for geometric figures; we describe some of geometric figures by using the properties of groups. The classification of some geometric figures by using the properties of some algebraic structures.

In this paper, we introduce the concept of fuzzy n-fold KUideal in KU-algebras, which is a generalization of fuzzy KU-ideal of KUalgebras and we obtain a few properties that is similar to the properties of fuzzy KU-ideal in KU-algebras, see [8]. Furthermore, we construct some algorithms for folding theory applied to KU-ideals in KU-algebras.

The concept of bipolar fuzzy ideals in a TM-algebra was introduced and some properties of these ideals are investigated. Also, a few relations between a bipolar fuzzy ideal and T-ideal are discussed. A new bipolar fuzzy set with a homomorphism of TM-algebra is defined. The Cartesian product of bipolar fuzzy T-ideals in Cartesian product TM-algebras is given.