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Prime ideals in autometrized algebras

1987; Springer Nature; Volume: 37; Issue: 1 Linguagem: Inglês

10.21136/cmj.1987.102135

1572-9141

Jiří Rachůnek,

Advanced Algebra and Logic

A system (A, +, ^, *) is called an autometrized algebra if (1) (A, +) is a commutative semigroup with zero element 0;(2) (A, ^) is an ordered set and У a, b,ce A; a^b=>abe A; a ^ b ^ 0 and a^b = Ooa = b, Va, b e A; a ^ b = b * a, \fa, b,CE A; a ^ с S (a -* b) + [b * c).An autometrized algebra [A, +, ^, *) is called a) an 1-algebra if (A, ^) is a lattice and Va, b, с e A; a + {b v c) = (a + b) v {a + c), a + {b A c) = (a + b) A (a -h c); b) semiregular if Vae^; a^O=>a*0 = a; c) normal if Va G Л; a ^ a * 0, Va, b, с, de A; (a + с) * (Ь + J) ^ (a * Ь) + (с * d), \fa, b, c, d e A; (a * c) * (b * d) ^ (a * Ь) + (c * J), Va, Ь e Л; (a ^ Ь => 3x ^ 0; a + X = b).