A ring [Formula: see text] is said to be clean if each element of can written as the sum a unit and an idempotent. weakly either or difference idempotent, feebly every text], where are orthogonal idempotents. Clearly, rings both them clean. In recent paper (J. Algebra Appl. 17 (2018) 1850111 (5 pp.)), McGoven characterized when group clean, distinct primes. this paper, we consider more general ...

The inverse Gröbner basis problem is to find the ideals that have a given monomial ideal as its initial ideal. We consider the problem of finding when the given monomial ideal is the initial ideal of a prime ideal. Kalkbrenner and Sturmfels (1995), in Theorem 1, prove that the radical of the initial ideal of a prime ideal is equi-dimensional and connected in codimension one or equivalently, the...

In this paper we characterize those hemirings for which each k-ideal is idempotent. We also characterize those hemirings for which each fuzzy k-ideal is idempotent. The space of prime k-ideals (fuzzy k-prime k-ideals) is topologized.