منابع مشابه
Commutative Subdirectly Irreducible Radical Rings
A ring R is radical if there is a ring S (with unit) such that R = J (S) (the Jacobson radical). We study the commutative subdirectly irreducible radical rings and show that such a ring is noetherian if and only if is finite. We present a reflection of the commutative radical rings into the category of the commutative rings and derive a lot of examples of the subdirectly irreducible radical rin...
متن کاملA note on irreducible Heegaard diagrams
We construct a Heegaard diagram of genus three for the real projective 3-space, which has no waves and pairs of complementary handles. The first example was given by Im and Kim but our diagram has smaller complexity. Furthermore the proof presented here is quite different to that of the quoted authors, and permits also to obtain a simple alternative proof of their result. Examples of irreducibl...
متن کاملStructure Theory of Faithful Rings, Iii. Irreducible Rings
The first two papers of this series1 were primarily concerned with a closure operation on the lattice of right ideals of a ring and the resulting direct-sum representation of the ring in case the closure operation was atomic. These results generalize the classical structure theory of semisimple rings. The present paper studies the irreducible components encountered in the direct-sum representat...
متن کاملNote on the Fundamental Theorem on Irreducible Non - Negative Matrices
1. Let A = [aii] be an n-th order irreducible non-negative matrix. As is very well-known, the matrix A has a positive characteristic root p (provided that n> I), which is simple and maximal in the sense that every characteristic root A satisfies I A I ~ p, and the characteristic vector x belonging to p may be chosen positive. These results, originally due to Frobenius, have been proved by Wiela...
متن کاملNote on Star Operations over Polynomial Rings
This paper studies the notions of star and semistar operations over a polynomial ring. It aims at characterizing when every upper to zero in R[X] is a ∗-maximal ideal and when a ∗-maximal ideal Q of R[X] is extended from R, that is, Q = (Q ∩ R)[X] with Q ∩R 6= 0, for a given star operation of finite character ∗ on R[X]. We also answer negatively some questions raised by Anderson-Clarke by const...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy
سال: 1946
ISSN: 0021-4280
DOI: 10.2183/pjab1945.22.333