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 m...

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

Let T(n) denote the number of n-simplices in a minimum cardinality decomposition of the n-cube into n-simplices. For n 1 we show that T(n) H(n), where H(n) is the ratio of the hyperbolic volume of the ideal cube to the ideal regular simplex. H(n) 1 2 6 n=2 (n+1) ? n+1 2 n!. Also lim n!1 p nH(n)] 1=n 0:9281. Explicit bounds for T(n) are tabulated for n 10, and we mention some other results on hy...

All rings in this paper are commutative with unity; we will deal mainly with integral domains. Let R be a ring with total quotient ring K. A fractional ideal I of R is invertible if II−1 = R; equivalently, I is a projective module of rank 1 (see, e.g., [Eis95, Section 11.3]). Here, I−1 = (R : I) = {x ∈ K |xI ⊆ R}. Moreover, a projective R-module of rank 1 is isomorphic to an invertible ideal. (...

Let X be an m × n matrix of indeterminates, m ≤ n, and T a new indeterminate. Consider the polynomial rings R0 = K[X] and R = R0[T ]. For a given positive integer t ≤ m, consider the ideal It = It(X) generated by the t-minors (i. e. the determinants of the t× t submatrices) of X . Using all these determinantal ideals, we define a new ideal J in R = R0[T ], which we call the generic graph constr...

All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M . Homogeneuous ideals of R(M) have the form I(+)N where I is an ideal of R, N a submodule of M such that IM ⊆ N . In particular, [N : M ] (+)N is a homogeneous ideal of R(M). The purpose of this paper is to investigate how properties of the ideal [N : M ](+)N are re...

We extend the basic fact that every ideal of a finite dimensional semisimple Lie algebra has a unique complement to the case of closed ideals of prosemisimple Lie algebras. We prove that if A is a closed ideal of a prosemisimple Lie algebra L = lim ←−−Ln (n ∈ N), where the Ln are finite dimensional semisimple Lie algebras, then there exists a unique ideal B of L such that L = A ⊕ B. Mathematics...

This paper explores finding the number nh of undirected hamiltonian paths in an undirected graph G = (V,E) using lumped/ideal circuits, specifically low-pass filters. Ideal analog computation allows one to computer nh in a short period of time, but in practice, precision problems disturb this ideal nature. A digital/algorithmic approach is proposed, and then it is shown that the approach/method...

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...

We describe an algorithm that, given a positive integer N , computes a Gröbner basis of the ideal of polynomial relations among Dedekind ηfunctions of level N , i. e., among the elements of {η(δ1τ), . . . , η(δnτ)} where 1 = δ1 < δ2 · · · < δn = N are the positive divisors of N . More precisely, we find a finite generating set (which is also a Gröbner basis) of the ideal kerφ where φ : Q[E1, . ...