We study prime algebras of quadratic growth. Our first result is that if A is a prime monomial algebra of quadratic growth then A has finitely many prime ideals P such that A/P has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the non...

This paper was motivated by a problem left by Herzog and Hibi, namely to classify all unmixed polymatroidal ideals. In the particular case of polymatroidal ideals corresponding to discrete polymatroids of Veronese type, i.e ideals of Veronese type, we give a complete description of the associated prime ideals and then, we show that such an ideal is unmixed if and only if it is CohenMacaulay. We...

Byun, H.L. and S. Watson, Prime and maximal ideals in subrings of C(X), Topology and its Applications 40 (1991) 45-62. The structure of ideals in the ring C(X) of continuous functions on a completely regular space X and its subring C*(X) consisting of the bounded functions is well known. In this paper we study the prime and maximal ideals in subrings A(X) of C(X) that contain C*(X). We show tha...

Preface . . . . . . . . . . . . . . . . . . . . . . . iii 1. Rings and Ideals . . . . . . . . . . . . . . . . . . . 1 2. Prime Ideals . . . . . . . . . . . . . . . . . . . . 6 3. Radicals . . . . . . . . . . . . . . . . . . . . . . 10 4. Modules . . . . . . . . . . . . . . . . . . . . . . 14 5. Exact Sequences . . . . . . . . . . . . . . . . . . . 20 6. Direct Limits . . . . . . . . . . . . . ....

Let R be a commutative radical Fréchet algebra having a nonnilpotent element a with a ∈ Ra. Then R contains a continuum of incomparable prime ideals. In [3], J. Esterle proved the following result; it is a main ingredient in his proof that epimorphisms from C0(Ω) onto Banach algebras are continuous. Theorem (Esterle). Let R be a commutative radical Banach algebra. Suppose that there exists a no...

Department of Mathematics, Jadavpur University Kolkata-700032, India manasi−[email protected] Abstract The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of Γsemigroups in order to obtain some characterization theorems. We also introduce the not...

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...

We prove that if the initial ideal of a prime ideal is Borel-fixed and the dimension of the quotient ring is less than or equal to two, then given any non-minimal associated prime ideal of the initial ideal it contains another associated prime ideal of dimension one larger. Let R = k[x1, x2, . . . , xr] be a polynomial ring over a field. We will say that an ideal I ⊆ R has the saturated chain p...

The central objects of study in this thesis are quantized coordinate algebras. These algebras originated in the 1980s in the work of Drinfeld and Jumbo and are noncommutative analogues of coordinate rings of algebraic varieties. The organic nature by which these algebras arose is of great interest to algebraists. In particular, investigating ring theoretic properties of these noncommutative alg...

Recently Yehuda Rav has given the concept of Semi prime ideals in a general lattice by generalizing the notion of 0-distributive lattices. In this paper we study several properties of these ideals in a general nearlattice and include some of their characterizations. We give some results regarding maximal filters and include a number of Separation properties in a general nearlattice with respect...