In this article‎, ‎we have characterized ideals in $C(X)$ in which‎ ‎every ideal is also an ideal (a $z$-ideal) of $C(X)$‎. ‎Motivated by‎ ‎this characterization‎, ‎we observe that $C_infty(X)$ is a regular‎ ‎ring if and only if every open locally compact $sigma$-compact‎ ‎subset of $X$ is finite‎. ‎Concerning prime ideals‎, ‎it is shown that‎ ‎the sum of every two prime (semiprime) ideals of e...

Background • Legendre Sequence For a prime p > 2 let (s n) be the Legendre sequence defined as s n = 1, n p = −1, 0, otherwise, n ≥ 0, where. p denotes the Legendre symbol. • Sidelnikov Sequence Let q be an odd prime power, g a primitive element of F q , and let η denote the quadratic character of F Background • Legendre Sequence For a prime p > 2 let (s n) be the Legendre sequence defined as s...

We characterize absorption in finite idempotent algebras by means of Jónsson absorption and cube term blockers. As an application we show that it is decidable whether a given subset is an absorbing subuniverse of an algebra given by the tables of its basic operations.

We study a simple sandpile model of active-absorbing state transition in which a particle can hop out of a site only if the number of particles at that site is above a certain threshold. We show that the active phase has a product measure whereas nontrivial correlations are found numerically in the absorbing phase. It is argued that the system relaxes to the latter phase slower than an exponent...

The cardinality of the minimal generating set of a module M i.e g(M) plays a very important role in the study of QTAG-Modules. Fuchs [1] mentioned the importance of upper and lower basic subgroups of primary groups. A need was felt to generalize these concepts for modules. An upper basic submodule B of a QTAG-Module M reveals much more information about the structure of M . We find that each ba...

primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...