Universal classes of Monadic Algebras

1976 ◽  
Vol 22 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Th. Lucas
Keyword(s):  
Universal Classes

Skolemizing algebraically closed universal classes of algebras

2015 ◽  
Vol 74 (3-4) ◽  
pp. 361-380
Author(s):  
Robert W. Quackenbush
Keyword(s):  
Universal Classes

On Radical Congruence Systems II

1998 ◽  
Vol 08 (03) ◽  
pp. 363-397
Author(s):  
T. E. Hall ◽  
Shuhua Zhang
Keyword(s):  
Universal Class ◽  
Universal Classes

This paper is a continuation of a paper of the same title by the first author and P. Weil. We first characterize the universal class of a radical congruence system. We then introduce the meet and the (limit) iteration of congruence systems. This enables us to generate new radical congruence systems from given congruence systems. Some interesting examples are presented. We finally determine the smallest radical congruence systems whose universal classes are N, LZ ◦ N, RZ ◦ N, and RB ◦ N respectively.

On the Existence of Free Structures over Universal Classes

1968 ◽  
Vol 36 (3-4) ◽  
pp. 135-140 ◽  
Author(s):  
George Grätzer
Keyword(s):  
Universal Classes

scholarly journals Some degeneracy and pathology in non-associative radical theory II

1981 ◽  
Vol 23 (3) ◽  
pp. 423-428 ◽  
Author(s):  
B. J. Gardner
Keyword(s):  
Associative Algebras ◽  
Additive Structure ◽  
Radical Theory ◽  
Commutative Algebras ◽  
Unital Ring ◽  
Universal Classes

It is shown that in the universal classes of(i) all commutative algebras,(ii) all anti-commutative algebras and(iii) all algebras satisfying x2 = 0 (over any commutative, associative, unital ring)the only radical classes with hereditary semi-simple classes are those for which membership is determined by additive structure. Some examples of non-hereditary semi-simple classes in the class of all power-associative algebras are also presented.

scholarly journals Universal classes of hash functions

1979 ◽  
Vol 18 (2) ◽  
pp. 143-154 ◽  
Author(s):  
J.Lawrence Carter ◽  
Mark N. Wegman
Keyword(s):  
Hash Functions ◽  
Universal Classes

ON BASE RADICAL OPERATORS FOR CLASSES OF FINITE ASSOCIATIVE RINGS

2018 ◽  
Vol 98 (2) ◽  
pp. 239-250 ◽  
Author(s):  
R. G. MCDOUGALL ◽  
L. K. THORNTON
Keyword(s):  
Maximum Order ◽  
Semisimple Class ◽  
Hereditary Radical ◽  
Complete Listing ◽  
Universal Classes ◽  
General Relations ◽  
Associative Rings

In this paper, class operators are used to give a complete listing of distinct base radical and semisimple classes for universal classes of finite associative rings. General relations between operators reveal that the maximum order of the semigroup formed is 46. In this setting, the homomorphically closed semisimple classes are precisely the hereditary radical classes and hence radical–semisimple classes, and the largest homomorphically closed subclass of a semisimple class is a radical–semisimple class.

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