We give a description of the minimal primes of the ideal generated by the 2×2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m×m minors of an m×n generic matrix when the characteristic of the ground field is zero. A key intermediate result is the proof that the ideals which appear as minimal primes are, in fact, prime ideals. This ...

We establish a necessary condition for a commutative Banach algebra A so that there exists a homomorphism θ from A into another Banach algebra such that the prime radical of the continuity ideal of θ is not a finite intersection of prime ideals in A. We prove that the prime radical of the continuity ideal of an epimorphism from A onto another Banach algebra (or of a derivation from A into a Ban...

We give an elementary proof that for a ring homomorphism A → B satisfying the property that every ideal in A is contracted from B the following property holds: for every chain of prime ideals p0 ⊂ . . . ⊂ pr in A there exists a chain of prime ideals q0 ⊂ . . . ⊂ qr in B such that qi ∩ A = pi. Mathematical Subject Classification (1991): 13B24. Let A and B be commutative rings and let φ : A → B b...

The notion of (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras is introduced. Some characterization theorems in (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras are derived. Also we study relation between (∈,∈ ∨q)-interval-valued fuzzy prime ideal and (∈ ∨q)-interval-valued fuzzy level prime ideals. Characterization of interval-valued fuzzy set to b...