We study algebras k[x1, ..., xn]/I which admit a grading by a subsemigroup of N such that every graded component is a one-dimensional k-vector space. V.I. Arnold and coworkers proved that for d = 1 and n ≤ 3 there are only finitely many isomorphism types of such A-graded algebras, and in these cases I is an initial ideal (in the sense of Gröbner bases) of a toric ideal. In this paper it is show...

Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...

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...

Abstract. Consider a height two ideal, I, which is minimally generated by m homogeneous forms of degree d in the polynomial ring R = k[x, y]. Suppose that one column in the homogeneous presenting matrix φ of I has entries of degree n and all of the other entries of φ are linear. We identify an explicit generating set for the ideal A which defines the Rees algebra R = R[It]; so R = S/A for the p...

In this paper, the author studied skeletal congruences θ^* of a distributive nearlattice S, where * represents pseudocomplement. Then described θ(I)^*, θ(I) is smallest congruence S containing n-ideal I as class and showed that I^+ n-kernel θ(I)^*. established following fundamental results: When n an upper element has shown n-kernels are precisely those n-ideals which intersection relative anni...

Let A be a commutative Noetherian ring of dimension n (n ≥ 3). Let I be a local complete intersection ideal in A[T ] of height n. Suppose I/I is free A[T ]/I-module of rank n and (A[T ]/I) is torsion inK0(A[T ]). It is proved in this paper that I is a set theoretic complete intersection ideal in A[T ] if one of the following conditions holds: (1) n ≥ 5, odd; (2) n is even, and A contains the fi...

An m×n ideal matrix is a periodic m×n binary matrix which satisfies the following two conditions: (1) each column of this matrix contains precisely one 1 and (2) if it is visualized as a dot pattern (with each dot representing a 1), then the number of overlapping dots at all actual shifts are 1 or 0. Let s(n) denote the smallest integer m such that an m × n ideal matrix exists. In this paper, w...

Micciancio defined a generalization of cyclic lattices, called ideal lattices. These lattices can be used in cryptosystems to decrease the number of parameters necessary to describe a lattice by a square root, making them more efficient. He proves that the computational intractability of classic lattice problems for these lattices gives rise to provably secure one-way and collision-resistant ha...