Introduction. L. Fuchs [2 ] has given for Noetherian rings a theory of the representation of an ideal as an intersection of primal ideals, the theory being in many ways analogous to the classical Noether theory. An ideal Q is primal if the elements not prime to Q form an ideal, necessarily prime, called the adjoint of Q. Primary ideals are necessarily primal, but not conversely. Analogous resul...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof continuous real-valued functions on $l$. we study the frame$mathfrak{o}(min(mathcal{r}l))$ of minimal prime ideals of$mathcal{r}l$ in relation to $beta l$. for $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals...

‎let $g$ be a finite group‎. ‎the degree pattern of $g$ denoted by‎ ‎$d(g)$ is defined as follows‎: ‎if $pi(g)={p_{1},p_{2},...,p_{k}}$ such that‎ ‎$p_{1}

2 Integral Domains 12 2.1 Factorization in Integral Domains . . . . . . . . . . . . . . . . 12 2.2 Euclidean Domains . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Principal Ideal Domains . . . . . . . . . . . . . . . . . . . . . 16 2.4 Fermat’s Two Squares Theorem . . . . . . . . . . . . . . . . . 17 2.5 Maximal Ideals and Prime Ideals . . . . . . . . . . . . . . . . 20 2.6 Unique Fact...

(Dual) hypergraphs have been used by Kimura, Rinaldo and Terai to characterize squarefree monomial ideals J with pd(R/J) ≤ μ(J) − 1, i.e. whose projective dimension equals the minimal number of generators of J minus 1. In this paper we prove sufficient and necessary combinatorial conditions for pd(R/J) ≤ μ(J)−2. The second main result is an effective explicit procedure to compute the projective...

We show that given any polynomial ring R over a field and any ideal J ⊂ R which is generated by three cubic forms, the projective dimension of R/J is at most 36. We also settle the question whether ideals generated by three cubic forms can have projective dimension greater than four, by constructing one with projective dimension equal to five.

We show that given any polynomial ring R over a field and any ideal J ⊂ R which is generated by three cubic forms, the projective dimension of R/J is at most 36. We also settle the question of whether ideals generated by three cubic forms can have projective dimension greater than four, by constructing one with projective dimension equal to five.

In this paper we introduce the notion of intuitionistic fuzzy prime, strongly prime, semiprime bi-ideals in ternary semigroup and look for some of their related characteristics. Also here we introduce irreducible and strongly irreducible intuitionistic fuzzy bi-ideals in a ternary semigroup. AMS subject classification: 20N10, 20M12, 04A72.

The hull kernel topology on the set of all prime α-ideals of an ADL is introduced. Many properties of this space are studied. Using the topological properties of the space of prime α-ideals various equivalent conditions for an ADL to be a -ADL are furnished. Mathematics Subject Classification: 06D99