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IDEALS AND DIRECT PRODUCT OF ZERO SQUARE RINGS

B. Satyanarayana, Goldoza Lungisile, Nagaraju Dasari

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Abstract

Abstract. We consider associative ring R (not necessarily commuta-tive). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were in-troduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided. 1.

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Abstract. We consider associative ring R (not necessarily commuta-tive). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were in-troduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided. 1.

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Available abstract

Abstract. We consider associative ring R (not necessarily commuta-tive). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were in-troduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided. 1.

Key concepts: Square (algebra), Mathematics, Zero (linguistics), Dimension (graph theory), Ideal (ethics), Zero divisor, Ring (chemistry), Simple ring

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